The generator matrix

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

generates a code of length 13 over Z2[X]/(X^4) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+34x^9+77x^10+228x^11+187x^12+1012x^13+170x^14+232x^15+65x^16+26x^17+9x^18+4x^19+3x^20

The gray image is a linear code over GF(2) with n=104, k=11 and d=36.
This code was found by Heurico 1.16 in 0.016 seconds.