The generator matrix

 1  1  1  1  1  1  X  0  1  1  1  1  1
 0  X  0 X^2+X X^2 X^3+X^2+X X^2+X  X X^3+X^2 X^3+X^2+X  X  X  0
 0  0 X^3+X^2  0 X^2 X^2 X^3 X^3  0 X^3+X^2 X^2 X^2  0
 0  0  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3  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+51x^10+42x^11+270x^12+304x^13+267x^14+36x^15+47x^16+1x^18+2x^19+2x^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.