The generator matrix

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

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+326x^11+2050x^12+5680x^13+14944x^14+19270x^15+15463x^16+5584x^17+1792x^18+370x^19+54x^20+2x^23

The gray image is a code over GF(2) with n=120, k=16 and d=44.
This code was found by Heurico 1.16 in 5.67 seconds.