The generator matrix

 1  0  0  0  1  1  1 X^2  1  X  1  1  1
 0  1  0  0  0  1 X^2+X+1  1 X^2+X  1  1 X+1  1
 0  0  1  0  1  1 X^2+X  1 X^2+1 X+1  X  X  0
 0  0  0  1  1  0 X^2+X+1 X+1 X^2+X  X  0  X  X
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0  0 X^2 X^2  0  0  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+317x^8+304x^9+2372x^10+2880x^11+7506x^12+5920x^13+7640x^14+2880x^15+2337x^16+304x^17+292x^18+14x^20+1x^24

The gray image is a linear code over GF(2) with n=52, k=15 and d=16.
This code was found by Heurico 1.16 in 7.88 seconds.