The generator matrix

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

generates a code of length 13 over Z2[X]/(X^4) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+82x^9+833x^10+2552x^11+7464x^12+10788x^13+7726x^14+2448x^15+735x^16+122x^17+9x^18+8x^19

The gray image is a linear code over GF(2) with n=104, k=15 and d=36.
This code was found by Heurico 1.16 in 1.53 seconds.