The generator matrix

 1  1  1  1  X  1  1 X^2  1  1  X  1  1
 0 X^3+X^2  0 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2  0  0  0 X^3  0
 0  0 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3  0
 0  0  0 X^3  0  0  0 X^3 X^3  0 X^3  0  0
 0  0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3  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+15x^8+36x^10+349x^12+256x^13+304x^14+44x^16+12x^18+7x^20

The gray image is a linear code over GF(2) with n=104, k=10 and d=32.
This code was found by Heurico 1.16 in -6.48e-008 seconds.