The generator matrix

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

generates a code of length 13 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+42x^8+192x^9+380x^10+1168x^11+1060x^12+2368x^13+1240x^14+1248x^15+293x^16+128x^17+44x^18+16x^19+12x^20

The gray image is a linear code over GF(2) with n=52, k=13 and d=16.
This code was found by Heurico 1.16 in 0.237 seconds.