The generator matrix
1 1 1 1 1 1 1 1 1 X 0 1 1
0 X 0 0 0 X X^2+X X X^2 X 0 X 0
0 0 X 0 X X X 0 0 X X X^2 X
0 0 0 X X 0 X X^2+X X 0 X^2 X X
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 X^2 0 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+33x^8+58x^9+90x^10+186x^11+375x^12+532x^13+422x^14+196x^15+66x^16+50x^17+30x^18+2x^19+5x^20+2x^22
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 0.0176 seconds.