The generator matrix

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

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+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 -1.01e-007 seconds.