The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X  1
 0 X^3+X^2  0 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2 X^3
 0  0 X^3+X^2 X^2  0 X^2 X^2 X^3 X^3 X^3  0 X^3 X^2
 0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 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+15x^10+42x^11+16x^12+368x^13+15x^14+36x^15+15x^16+1x^18+2x^19+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 -1.01e-007 seconds.