The generator matrix

 1  0  0  1  1  1 3X+2  1  1 2X  1  1  1  1  1
 0  1  0 2X+2  1 3X+3  1 3X 3X+2  1 X+1  3  1 3X+1  0
 0  0  1 3X+3  1  X X+1 3X+2 2X+3  X X+1 2X+2 X+3 2X 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+100x^12+432x^13+827x^14+1468x^15+733x^16+376x^17+124x^18+28x^19+6x^20+1x^22

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 0.015 seconds.