The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+353x^12+1272x^14+768x^15+1410x^16+264x^18+27x^20+1x^24

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 1.47 seconds.