The generator matrix

 1  0  0  0  1  1  1 X^2  0  1 X^2+X  1  1
 0  1  0  0  0 X^2+1 X+1  1  1 X^2+1  1  1  0
 0  0  1  0  1  1  X X+1  X X+1  0 X^2+1  0
 0  0  0  1  1  X  1  1 X+1  X X+1 X^2+X X^2
 0  0  0  0  X  0  0 X^2  X X^2+X X^2  X  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+124x^8+324x^9+897x^10+1784x^11+3056x^12+3944x^13+3103x^14+1872x^15+903x^16+244x^17+95x^18+24x^19+12x^20+1x^22

The gray image is a linear code over GF(2) with n=52, k=14 and d=16.
This code was found by Heurico 1.13 in 0.281 seconds.