The generator matrix

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

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+123x^12+160x^13+322x^14+832x^15+342x^16+160x^17+92x^18+13x^20+2x^22+1x^24

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 0.141 seconds.