The generator matrix

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

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+121x^8+352x^10+192x^11+1066x^12+640x^13+1040x^14+192x^15+397x^16+80x^18+14x^20+1x^24

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 0.0564 seconds.