The generator matrix

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

generates a code of length 13 over Z2[X]/(X^3) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+6x^11+15x^12+84x^13+15x^14+6x^15+1x^26

The gray image is a linear code over GF(2) with n=52, k=7 and d=22.
This code was found by Heurico 1.16 in 0.000657 seconds.