The generator matrix

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

generates a code of length 15 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+18x^14+20x^15+19x^16+4x^17+2x^18

The gray image is a code over GF(2) with n=120, k=6 and d=56.
This code was found by Heurico 1.16 in -3.24e-008 seconds.