The generator matrix

 1  0  0  0  0  1  1  1  1  1  1  X  1
 0  1  0  0  0  0 X^2+1 X+1 X^2+1 X^2+X+1  X  1  0
 0  0  1  0  0  1 X+1  X  0  1  X  X  X
 0  0  0  1  0  1  X X+1  0 X^2+1 X+1 X^2  0
 0  0  0  0  1  1  0 X^2  1 X^2+1 X^2+X+1  X X^2+X+1
 0  0  0  0  0  X  X  X X^2+X X^2 X^2  X X^2+X

generates a code of length 13 over Z2[X]/(X^3) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+138x^7+754x^8+2486x^9+6994x^10+15306x^11+25108x^12+29558x^13+24862x^14+15534x^15+7069x^16+2386x^17+718x^18+126x^19+28x^20+2x^21+2x^22

The gray image is a linear code over GF(2) with n=52, k=17 and d=14.
This code was found by Heurico 1.13 in 7 seconds.