The generator matrix

 1  0  1  1  1 3X+2  1  1 2X  1  1 3X  1  1 2X+2
 0  1 X+1 3X+2  3  1 3X+3 2X  1 3X 2X+3  1 X+1 X+3 2X
 0  0 2X+2  0  2 2X 2X+2  2 2X+2 2X  0 2X  0 2X 2X+2
 0  0  0 2X  0 2X 2X 2X  0 2X 2X  0  0  0  0
 0  0  0  0 2X  0 2X  0  0 2X 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+202x^12+384x^13+960x^14+1024x^15+951x^16+384x^17+160x^18+30x^20

The gray image is a code over GF(2) with n=120, k=12 and d=48.
This code was found by Heurico 1.16 in 0.046 seconds.