The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 0 1 1 1 0 1 X 1 1 1 1 0 1 1 1 1 X 1 1 1 1 1 1 X^2 1 0 1 1 X 1 X^2 X 1 1 0 X 1 1 1
0 X 0 0 0 0 0 X^2 X^2 X X^2+X X X X X^2+X X 0 X^2+X X^2 X X^2 X 0 X X^2 X^2+X X 0 X^2+X X^2 X^2+X 0 0 X^2 0 X X X^2+X X^2 X^2 X^2+X 0 0 X^2+X X 0 X^2 0 X X X X^2 0 X^2 X^2+X 0 X X 0 X X^2 X^2 X^2 X X^2+X 0 X X X 0 X^2 X^2+X X^2+X 0 X X^2+X X 0 X^2+X X^2 X 0 0 X^2+X 0 X X^2 X^2+X X X^2
0 0 X 0 0 X^2 X^2+X X X X X X X^2+X 0 0 0 X^2 X^2 X^2+X X X^2 0 0 X^2+X X^2 X^2 X X^2+X 0 X X X^2+X X X^2+X X^2+X 0 X^2 0 0 X^2 X^2+X X^2 X X 0 0 0 0 X X X X X X^2+X X^2 X^2 X X^2+X X X X^2+X 0 X X^2 X^2+X 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X 0 X^2 X^2+X X 0 X^2 X 0 X^2+X 0 X X^2 X^2+X X^2
0 0 0 X 0 X^2+X X^2+X X X^2 X^2+X X^2+X 0 0 X X X^2 X X^2 X^2+X 0 X^2+X 0 X^2 X X^2 X X X^2 X X 0 0 X^2 X 0 X^2+X X^2 X^2+X X X^2 0 0 X X^2+X 0 X^2+X 0 X^2 0 X^2+X X 0 0 X^2 X X X^2 X^2 X^2+X X^2+X X^2+X X X X 0 X^2+X X^2 X^2 X X^2+X X^2+X X^2+X X X X^2+X X X 0 X X X X X^2+X X^2+X 0 X^2+X 0 X^2 X X^2+X
0 0 0 0 X X X^2 X^2+X X X^2+X X^2 X^2 X X^2 X^2+X X X X^2 X^2 X^2+X 0 X^2+X 0 X^2+X X^2+X X^2+X 0 X^2+X 0 X 0 X^2 0 X^2+X X 0 X^2 X^2+X X^2+X 0 X^2+X X^2+X 0 X^2+X X X^2 0 X 0 X^2 X^2+X X^2 X^2+X 0 0 0 X X^2 0 0 X^2+X X X^2+X X^2 0 X X^2+X X X X^2 X^2 X^2 X^2 X^2 X^2+X X X 0 X^2+X 0 0 X X X 0 X^2 X^2 X 0 X^2+X
generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.
Homogenous weight enumerator: w(x)=1x^0+40x^82+66x^83+101x^84+98x^85+115x^86+184x^87+211x^88+218x^89+144x^90+182x^91+184x^92+128x^93+105x^94+48x^95+49x^96+48x^97+33x^98+22x^99+17x^100+14x^101+8x^102+8x^103+11x^104+6x^105+2x^106+2x^107+2x^108+1x^154
The gray image is a linear code over GF(2) with n=360, k=11 and d=164.
This code was found by Heurico 1.16 in 0.821 seconds.