The generator matrix

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

generates a code of length 15 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+80x^11+506x^12+1392x^13+3620x^14+5232x^15+3559x^16+1424x^17+472x^18+64x^19+30x^20+4x^22

The gray image is a code over GF(2) with n=120, k=14 and d=44.
This code was found by Heurico 1.16 in 0.421 seconds.