The generator matrix
1 0 1 1 1 X 1 1 1 1 0 1 1
0 1 1 X^2 X^3+X+1 1 X^2+X+1 X^3+X^2+X X^3+1 X^3+X^2+X+1 0 X^2 X^3+X^2+X
0 0 X X X^2 X X^3+X X^2 X^2+X 0 X X^3+X^2 X^3+X^2
0 0 0 X^3 0 X^3 0 X^3 X^3 X^3 0 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+115x^10+384x^11+778x^12+1552x^13+794x^14+352x^15+91x^16+16x^17+11x^18+2x^20
The gray image is a linear code over GF(2) with n=104, k=12 and d=40.
This code was found by Heurico 1.16 in 0.031 seconds.