The generator matrix

 1  0  1  1  1  0  1  1  1  1  1  1  1
 0  1  1  0 X+1  1  X  0 X^2+X+1 X+1 X^2+X X^2  0
 0  0  X X^2+X  0 X^2+X  X  0  X X^2  0  X  0
 0  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2  0
 0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  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+35x^8+32x^9+119x^10+176x^11+487x^12+352x^13+485x^14+176x^15+116x^16+32x^17+33x^18+1x^20+3x^22

The gray image is a linear code over GF(2) with n=52, k=11 and d=16.
This code was found by Heurico 1.16 in 0.013 seconds.