The generator matrix

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

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+26x^8+93x^10+128x^11+264x^12+264x^14+128x^15+93x^16+26x^18+1x^26

The gray image is a linear code over GF(2) with n=52, k=10 and d=16.
This code was found by Heurico 1.16 in 0.0049 seconds.