The generator matrix
1 0 1 1 1 X^2+X 1 1 1 1 1 1 1
0 1 X+1 X^2+X X^2+1 1 0 X^2+X X^2+X X X+1 X^2+1 0
0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0
0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0
generates a code of length 13 over Z2[X]/(X^3) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+13x^10+40x^11+51x^12+48x^13+49x^14+40x^15+11x^16+1x^18+1x^20+1x^22
The gray image is a linear code over GF(2) with n=52, k=8 and d=20.
This code was found by Heurico 1.16 in 0.00112 seconds.