The generator matrix

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

generates a code of length 15 over Z4[X]/(X^2+2X+2) 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 3.62e-008 seconds.