The generator matrix

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

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+21x^10+72x^11+331x^12+176x^13+329x^14+72x^15+19x^16+1x^18+1x^20+1x^22

The gray image is a linear code over GF(2) with n=104, k=10 and d=40.
This code was found by Heurico 1.16 in 3.81e-009 seconds.