The generator matrix

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

generates a code of length 15 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+48x^13+86x^14+272x^15+63x^16+16x^17+9x^18+16x^19+1x^26

The gray image is a code over GF(2) with n=120, k=9 and d=52.
This code was found by Heurico 1.16 in 0 seconds.