The generator matrix
1 0 0 0 1 1 1 X^2 0 1 X^2+X 1 1
0 1 0 0 0 X^2+1 X+1 1 1 X^2+1 1 1 0
0 0 1 0 1 1 X X+1 X X+1 0 X^2+1 0
0 0 0 1 1 X 1 1 X+1 X X+1 X^2+X X^2
0 0 0 0 X 0 0 X^2 X X^2+X X^2 X 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+124x^8+324x^9+897x^10+1784x^11+3056x^12+3944x^13+3103x^14+1872x^15+903x^16+244x^17+95x^18+24x^19+12x^20+1x^22
The gray image is a linear code over GF(2) with n=52, k=14 and d=16.
This code was found by Heurico 1.13 in 0.281 seconds.