The generator matrix

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

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+79x^8+236x^9+499x^10+876x^11+1457x^12+1864x^13+1499x^14+904x^15+476x^16+204x^17+81x^18+12x^19+3x^20+1x^22

The gray image is a linear code over GF(2) with n=52, k=13 and d=16.
This code was found by Heurico 1.11 in 0.078 seconds.