The generator matrix

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

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+172x^11+950x^12+2966x^13+7306x^14+9898x^15+7503x^16+2884x^17+868x^18+200x^19+10x^20+6x^21+2x^22+2x^23

The gray image is a code over GF(2) with n=120, k=15 and d=44.
This code was found by Heurico 1.16 in 1.59 seconds.