The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  X  X  X  X
 0 X^2+2  0 X^2+2  2 X^2  2 X^2 X^2+2 X^2+2  0  2 X^2  0  2
 0  0  2  2  2  2  0  0  0  2  2  2  2  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+14x^14+96x^15+15x^16+2x^22

The gray image is a code over GF(2) with n=120, k=7 and d=56.
This code was found by Heurico 1.16 in 3.62e-008 seconds.