The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1  0 X^3+X X^2+1 X+1
 0  0 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3  0
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0
 0  0  0  0 X^3 X^3 X^3 X^3  0 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+40x^10+144x^11+569x^12+544x^13+565x^14+144x^15+37x^16+2x^18+1x^20+1x^22

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 1.05e-007 seconds.