The generator matrix
1 0 0 1 1 1 X^3+X 1 1 X^2+X 1 1 1
0 1 0 X^2 1 X^3+X+1 1 X^2 X^3+X 1 X^2+X X^3+X^2 X^3+X^2+1
0 0 1 X^2+X+1 1 X^2 X^2+1 X X^2+X 0 X^3 X^2+1 X^2+X+1
0 0 0 X^3 X^3 X^3 0 0 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+157x^10+844x^11+1608x^12+3006x^13+1594x^14+802x^15+151x^16+18x^17+9x^18+2x^19
The gray image is a linear code over GF(2) with n=104, k=13 and d=40.
This code was found by Heurico 1.16 in 0.157 seconds.