The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^3 X^3 X^3+X^2  0
 0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0
 0  0  0 X^3 X^3 X^3 X^3  0 X^3  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+1x^10+16x^11+30x^12+160x^13+30x^14+16x^15+1x^18+1x^24

The gray image is a linear code over GF(2) with n=104, k=8 and d=40.
This code was found by Heurico 1.16 in -3.24e-008 seconds.