The generator matrix

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

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+47x^12+48x^13+304x^14+224x^15+312x^16+48x^17+32x^18+5x^20+3x^24

The gray image is a code over GF(2) with n=120, k=10 and d=48.
This code was found by Heurico 1.16 in 0.016 seconds.