The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0 2X  0  0  0 2X  0  0 2X 2X  0  0 2X 2X 2X
 0  0 2X  0  0 2X  0 2X 2X  0 2X 2X 2X 2X  0
 0  0  0 2X  0 2X 2X 2X  0  0 2X  0  0 2X 2X
 0  0  0  0 2X 2X 2X  0  0 2X 2X 2X 2X  0  0

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

Homogenous weight enumerator: w(x)=1x^0+15x^14+224x^15+15x^16+1x^30

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 0 seconds.