The generator matrix

 1  1  1  1  1  1  1  X X^3  X  X  1  1
 0  X  0  X X^3  0 X^3+X X^2 X^3+X^2  X X^2+X  X X^2+X
 0  0  X  X X^2 X^2+X X^2+X  X  X  X X^3+X^2+X X^3+X^2 X^2+X
 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+58x^10+262x^11+390x^12+644x^13+388x^14+232x^15+55x^16+12x^17+2x^18+2x^19+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 0.016 seconds.