The generator matrix

 1  1  1  1  1  1  1  1  1  1 X^2  X  1
 0  X X^3+X^2 X^2+X  0 X^2+X  0 X^2+X X^3 X^3+X^2+X X^3+X^2 X^2+X  0
 0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0  0
 0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  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+18x^10+50x^11+94x^12+190x^13+91x^14+46x^15+17x^16+2x^17+2x^18+1x^22

The gray image is a linear code over GF(2) with n=104, k=9 and d=40.
This code was found by Heurico 1.16 in -3.24e-008 seconds.