The generator matrix

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

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+98x^10+112x^11+486x^12+672x^13+476x^14+112x^15+71x^16+18x^18+2x^20

The gray image is a linear code over GF(2) with n=104, k=11 and d=40.
This code was found by Heurico 1.16 in 10.8 seconds.