The generator matrix

 1  1  1  1  X  0  1  1  1  1  X  1  1
 0  X X^3+X^2 X^2+X X^2+X  X  0  0 X^3+X^2 X^3+X^2 X^3+X^2  0  0
 0  0 X^3  0  0  0  0 X^3 X^3 X^3  0 X^3  0
 0  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3  0 X^3 X^3  0 X^3  0  0  0
 0  0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3  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+23x^8+76x^10+64x^11+557x^12+640x^13+512x^14+64x^15+84x^16+20x^18+7x^20

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 3.62e-008 seconds.