The generator matrix
1 1 1 1 1 1 1 1 X 1 X 1 1
0 X 0 0 0 0 0 X^2 X^2+X X X^2 X^2+X 0
0 0 X 0 0 X^2 X^2+X X X^2+X X X 0 0
0 0 0 X 0 X^2+X X^2+X X X^2 X^2+X X^2+X 0 0
0 0 0 0 X X X^2 X X X^2+X X 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+74x^8+32x^9+73x^10+216x^11+342x^12+528x^13+399x^14+224x^15+81x^16+16x^17+39x^18+8x^19+14x^20+1x^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 0.0207 seconds.