The generator matrix

 1  0  0  0  1  1  1 X^3+X X^3+X X^2+X X^3+X^2+X X^3  1
 0  1  0  0 X^2 X^2+1  1  1  1 X^2+X X^2  1  0
 0  0  1  0 X^2+1  1  X X+1  1  0  1  X  0
 0  0  0  1  1  X X+1 X^2+1 X^2  1 X^2+1 X^2+X  0
 0  0  0  0 X^3  0 X^3  0 X^3 X^3  0  0  0

generates a code of length 13 over Z2[X]/(X^4) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+181x^8+818x^9+3387x^10+11908x^11+27080x^12+44188x^13+27304x^14+11904x^15+3296x^16+802x^17+187x^18+12x^19+2x^20+2x^22

The gray image is a linear code over GF(2) with n=104, k=17 and d=32.
This code was found by Heurico 1.16 in 13 seconds.