The generator matrix

 1  1  1  1  1  1  1  1  X  1  1  X  X  0  X
 0  X  0  X 2X  0 3X+2  2 X+2  2 3X+2 X+2 2X+2 2X 2X+2
 0  0  X  X 2X+2 3X+2 3X+2 2X+2 2X+2  0 2X  2  X  X 2X+2
 0  0  0 2X 2X 2X  0 2X  0 2X  0  0  0 2X  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+156x^12+112x^13+482x^14+544x^15+499x^16+112x^17+124x^18+16x^20+2x^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.