The generator matrix

 1  1  1  1  1  1  X  1  X  X X^2  1  X X^2  1
 0  2  0  2  0  2  2  0  0  2  2  2  0  0  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+1x^14+22x^15+1x^16+6x^17+1x^18

The gray image is a code over GF(2) with n=120, k=5 and d=56.
This code was found by Heurico 1.16 in 6.87e-008 seconds.