The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^2+1 X+1 X+1  0
 0  0 X^3  0  0  0 X^3 X^3  0  0 X^3  0  0
 0  0  0 X^3  0  0 X^3  0  0 X^3 X^3  0  0
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0
 0  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0  0

generates a code of length 13 over Z2[X]/(X^4) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+10x^8+24x^9+80x^10+320x^11+1060x^12+1104x^13+1064x^14+320x^15+77x^16+24x^17+8x^18+4x^20

The gray image is a linear code over GF(2) with n=104, k=12 and d=32.
This code was found by Heurico 1.16 in 0.016 seconds.