The generator matrix

 1  1  1  1  X  0  1  1  X  1  1  1  1
 0  X  0 X^2+X  X  X  0 X^2+X  X  0  0  0  0
 0  0 X^2  0  0  0  0  0  0 X^2  0  0 X^2
 0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2
 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  0  0
 0  0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2
 0  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2
 0  0  0  0  0  0  0  0 X^2 X^2 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+26x^6+83x^8+284x^10+256x^11+1132x^12+512x^13+1152x^14+256x^15+299x^16+68x^18+20x^20+6x^22+1x^24

The gray image is a linear code over GF(2) with n=52, k=12 and d=12.
This code was found by Heurico 1.16 in 0.0304 seconds.