The generator matrix

 1  1  1  1  1  1  X  X  X X^2  X X^2  1
 0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0

generates a code of length 13 over Z2[X]/(X^4) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+1x^12+22x^13+2x^14+6x^15

The gray image is a linear code over GF(2) with n=104, k=5 and d=48.
This code was found by Heurico 1.16 in 0.016 seconds.