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.