The generator matrix

 1  1  1  1  1  1  1  1  X  0  X X^2+2  X  2  1
 0  X X^2+2 X^2+X  2 X^2+X+2 X^2 X+2 X^2+X  X X+2  X X^2+X+2  X  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+30x^14+64x^15+30x^16+1x^18+1x^20+1x^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 0.016 seconds.