The generator matrix
1 1 1 1 1 1 1 1 1 1 X 1 1
0 X 0 X^2+X 0 X^2 X^2+X X^2+X 0 X^2+X X^2+X X^2 0
0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2
0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2
0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 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+23x^10+74x^12+64x^13+70x^14+20x^16+3x^18+1x^24
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 0.00131 seconds.