The generator matrix

 1  0  1  1  1 X+2  1  1  1  1 2X+2 3X  1  1  1
 0  1 X+1 X+2  3  1 2X+2 3X+3 3X 2X+1  1  1 2X 3X+2  2

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

Homogenous weight enumerator: w(x)=1x^0+78x^14+96x^15+79x^16+2x^22

The gray image is a code over GF(2) with n=120, k=8 and d=56.
This code was found by Heurico 1.16 in 3.81e-009 seconds.