The generator matrix

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

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+42x^9+132x^10+352x^11+840x^12+1398x^13+804x^14+336x^15+135x^16+46x^17+8x^18+2x^21

The gray image is a linear code over GF(2) with n=104, k=12 and d=36.
This code was found by Heurico 1.16 in 0.031 seconds.