The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  X  X
 0  X  0  0  0  X X^2+X  X  0  0 X^2 X^2  0
 0  0  X  0  X  X X^2+X  0  0  X  X  0  0
 0  0  0  X  X  0 X^2+X  X  X  X  0  X  0
 0  0  0  0 X^2  0  0  0  0  0 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2
 0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2
 0  0  0  0  0  0  0  0 X^2 X^2  0  0 X^2

generates a code of length 13 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+64x^6+64x^7+247x^8+384x^9+1160x^10+1472x^11+2624x^12+4352x^13+2616x^14+1472x^15+1175x^16+384x^17+248x^18+64x^19+48x^20+8x^22+1x^24

The gray image is a linear code over GF(2) with n=52, k=14 and d=12.
This code was found by Heurico 1.16 in 0.433 seconds.