The generator matrix

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

generates a code of length 13 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+63x^4+67x^6+506x^8+501x^10+2048x^11+910x^12+8192x^13+910x^14+2048x^15+501x^16+506x^18+67x^20+63x^22+1x^26

The gray image is a linear code over GF(2) with n=52, k=14 and d=8.
This code was found by Heurico 1.16 in 0.276 seconds.