The generator matrix
1 1 1 1 1 1 1 1 1 X 1 1 1
0 X 0 0 0 0 0 0 0 X X^2 X^2+X X^2
0 0 X 0 0 0 X X^2+X X X X X X^2
0 0 0 X 0 X X X^2+X 0 0 0 X^2 0
0 0 0 0 X X 0 X^2+X X 0 X^2 X^2+X 0
0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2
0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2
0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2
generates a code of length 13 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+32x^6+96x^7+199x^8+380x^9+604x^10+944x^11+3248x^12+5356x^13+3276x^14+928x^15+615x^16+404x^17+180x^18+80x^19+32x^20+4x^21+4x^22+1x^24
The gray image is a linear code over GF(2) with n=52, k=14 and d=12.
This code was found by Heurico 1.16 in 0.451 seconds.