The generator matrix

 1  1  1  1  1  1  X X^2  X  X  1  1  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2  0
 0  0 X^3  0  0  0  0  0 X^3 X^3 X^3  0  0
 0  0  0 X^3  0  0  0  0 X^3 X^3  0 X^3  0
 0  0  0  0 X^3  0  0 X^3  0 X^3 X^3  0  0
 0  0  0  0  0 X^3  0 X^3  0 X^3  0 X^3  0
 0  0  0  0  0  0 X^3 X^3 X^3 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+26x^8+16x^9+93x^10+64x^11+520x^12+608x^13+520x^14+64x^15+93x^16+16x^17+26x^18+1x^26

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.