The generator matrix

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

generates a code of length 15 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+304x^12+808x^13+1874x^14+2248x^15+1883x^16+760x^17+268x^18+24x^19+20x^20+2x^22

The gray image is a code over GF(2) with n=120, k=13 and d=48.
This code was found by Heurico 1.16 in 0.11 seconds.