The generator matrix

 1  0  1  1  1 X^2  1  1  0  1 X^2  1  1
 0  1  1  0  1  1 X+1 X^2  1  0  X  0  0
 0  0  X  0  0  0  0  X X^2  X X^2  X  0
 0  0  0  X  0  X  X  X X^2+X X^2+X  X  X  0
 0  0  0  0  X X^2  X X^2+X X^2+X X^2 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+76x^8+122x^9+205x^10+440x^11+692x^12+910x^13+839x^14+480x^15+175x^16+86x^17+43x^18+8x^19+16x^20+2x^21+1x^22

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 0.0587 seconds.