The generator matrix

 1  1  1  1  1  1  1  1  X  X  1  1 X^2
 0 X^3+X^2  0 X^2  0 X^3 X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2
 0  0 X^3+X^2 X^2  0 X^2 X^2 X^2 X^3 X^2  0 X^3 X^3
 0  0  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0
 0  0  0  0 X^3 X^3  0 X^3  0  0 X^3  0 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+58x^10+32x^11+273x^12+320x^13+249x^14+32x^15+45x^16+12x^18+1x^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 0.062 seconds.