The generator matrix

 1  1  1  1  1  1  1  1  X  1  X  1  1
 0 X^3+X^2  0 X^2  0  0 X^2 X^2 X^3 X^3 X^3 X^3  0
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2  0 X^2 X^2 X^2 X^2  0
 0  0  0 X^3  0  0 X^3  0 X^3  0  0 X^3  0
 0  0  0  0 X^3  0  0  0 X^3 X^3  0 X^3  0
 0  0  0  0  0 X^3 X^3 X^3  0 X^3  0  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+33x^8+24x^9+31x^10+128x^11+59x^12+1488x^13+67x^14+128x^15+34x^16+24x^17+29x^18+1x^20+1x^22

The gray image is a linear code over GF(2) with n=104, k=11 and d=32.
This code was found by Heurico 1.16 in 0.016 seconds.