The generator matrix

 1  1  1  1  1  1  1  X  1  1  1  0  0  1  1
 0  X  0  X 2X 3X  2 3X  2 X+2 X+2  X  0 2X+2  0
 0  0  X  X 2X+2 3X+2 3X+2 2X 3X  2  0 3X+2  X  2  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+34x^12+128x^13+168x^14+400x^15+140x^16+96x^17+32x^18+16x^19+8x^20+1x^24

The gray image is a code over GF(2) with n=120, k=10 and d=48.
This code was found by Heurico 1.16 in 3.62e-008 seconds.