The generator matrix

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

generates a code of length 13 over Z2[X]/(X^4) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+122x^10+256x^11+974x^12+1408x^13+964x^14+256x^15+95x^16+18x^18+2x^20

The gray image is a linear code over GF(2) with n=104, k=12 and d=40.
This code was found by Heurico 1.16 in 102 seconds.