The generator matrix

 1  0  0  1  1  1  X  1  1 X^2+X X^2+X  X  1
 0  1  0  1 X^2+X X^2+X+1  1 X^2 X^2+1  1  0  0  0
 0  0  1  1 X^2+X+1 X^2+X  1  X X+1  0  1  0  0
 0  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2  0
 0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0
 0  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 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+32x^8+88x^9+220x^10+528x^11+650x^12+1072x^13+640x^14+528x^15+207x^16+88x^17+36x^18+6x^20

The gray image is a linear code over GF(2) with n=52, k=12 and d=16.
This code was found by Heurico 1.16 in 0.039 seconds.