The generator matrix
1 1 1 1 1 1 1 1
0 X 0 0 0 X 0 0
0 0 X 0 0 X 0 0
0 0 0 X 0 X 0 0
0 0 0 0 X X 0 0
0 0 0 0 0 X^2 0 0
0 0 0 0 0 0 X^2 0
0 0 0 0 0 0 0 X^2
generates a code of length 8 over Z2[X]/(X^3) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+48x^2+428x^4+1936x^6+11558x^8+1936x^10+428x^12+48x^14+1x^16
The gray image is a linear code over GF(2) with n=32, k=14 and d=4.
This code was found by Heurico 1.16 in 0.11 seconds.