The generator matrix

 1  0  0  0  1  1  1 X^2  1  1 X^3+X X^2+X  1
 0  1  0  0 X^2 X^3+1 X^2+X+1  1 X^2+X  1  1  1 X^2
 0  0  1  0 X^2+1  1  X X^2+1  1 X^3+X+1 X^2+X+1 X^2  0
 0  0  0  1  1 X^2 X+1 X^2+X+1 X^3+X X^3+X^2+1  X X+1  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+210x^9+1475x^10+5500x^11+14562x^12+21804x^13+15042x^14+5360x^15+1283x^16+274x^17+19x^18+4x^19+2x^20

The gray image is a linear code over GF(2) with n=104, k=16 and d=36.
This code was found by Heurico 1.16 in 5.13 seconds.