The generator matrix
1 1 1 1 1 1 1 1 X X 1 1 X^2
0 X^3+X^2 0 X^2 0 X^3 X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2
0 0 X^3+X^2 X^2 0 X^2 X^2 X^2 X^3 X^2 0 X^3 X^3
0 0 0 X^3 0 0 0 X^3 0 X^3 X^3 X^3 0
0 0 0 0 X^3 X^3 0 X^3 0 0 X^3 0 X^3
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+32x^11+273x^12+320x^13+249x^14+32x^15+45x^16+12x^18+1x^20+1x^22
The gray image is a linear code over GF(2) with n=104, k=10 and d=40.
This code was found by Heurico 1.16 in 0.062 seconds.