The generator matrix

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

generates a code of length 13 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+3x^12+22x^13+3x^14+2x^17+1x^18

The gray image is a linear code over GF(2) with n=52, k=5 and d=24.
This code was found by Heurico 1.16 in 0.000436 seconds.