The generator matrix

 1  0  1  1  1 X+2  1  1 2X+2  1  1 3X 2X+2  0  0
 0  1 X+1 X+2  3  1 2X+2 3X+3  1 3X 2X+1  1  X  X  X
 0  0 2X  0  0 2X 2X  0  0 2X 2X  0 2X  0  0
 0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0 2X
 0  0  0  0 2X 2X 2X 2X  0 2X  0  0 2X 2X 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+95x^12+128x^13+672x^14+256x^15+687x^16+128x^17+64x^18+16x^20+1x^28

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 0.093 seconds.