The generator matrix
1 0 1 1 1 X^2 X 1 1 1 1 X^2+X 1 1 1 1 1 1 1 1 1 X^2+X X^2 1 1 1
0 1 1 X^2+X X^2+X+1 1 1 X^2 X^2+1 X X+1 1 X^2 X^2+1 X 0 X X X^2+X+1 X+1 X+1 1 1 X^2 X^2+X+1 1
0 0 X 0 X^2+X X X^2+X X X^2 X^2+X X^2 0 X^2+X X^2 X^2+X 0 X X^2 X 0 X X^2 X^2+X X^2 X X
0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0
0 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0
generates a code of length 26 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.
Homogenous weight enumerator: w(x)=1x^0+95x^22+48x^23+193x^24+80x^25+213x^26+80x^27+174x^28+48x^29+73x^30+9x^32+3x^34+6x^36+1x^40
The gray image is a linear code over GF(2) with n=104, k=10 and d=44.
This code was found by Heurico 1.16 in 0.0228 seconds.