The generator matrix
1 1 1 1 1 1 X X X 0 X X X
0 X 0 X 0 0 X X^2+X X^2 0 X^2 X^2 0
0 0 X X 0 X^2+X X 0 X X X X 0
0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2
0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2
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 X^2 X^2 X^2 X^2 X^2 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+78x^8+32x^9+161x^10+128x^11+528x^12+192x^13+528x^14+128x^15+161x^16+32x^17+78x^18+1x^26
The gray image is a linear code over GF(2) with n=52, k=11 and d=16.
This code was found by Heurico 1.16 in 0.0148 seconds.