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.