The generator matrix

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

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+31x^6+32x^7+91x^8+192x^9+480x^10+864x^11+1444x^12+1920x^13+1446x^14+864x^15+483x^16+192x^17+88x^18+32x^19+28x^20+3x^22+1x^24

The gray image is a linear code over GF(2) with n=52, k=13 and d=12.
This code was found by Heurico 1.16 in 0.0844 seconds.