The generator matrix

 1  0  1  1  1  2  1  1  X  1  1  1  X  1  1
 0  1  1 2X+2 3X+1  1 3X 2X+1  1 X+2  0  X 2X  X 2X
 0  0  X 3X 2X+2 3X+2 3X+2 2X 3X  2  2  0 X+2 2X+2 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+33x^12+244x^13+430x^14+708x^15+338x^16+222x^17+55x^18+8x^19+4x^20+2x^21+3x^22

The gray image is a code over GF(2) with n=120, k=11 and d=48.
This code was found by Heurico 1.16 in 0.016 seconds.