The generator matrix

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

generates a code of length 16 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+368x^11+1682x^12+7822x^13+24631x^14+57292x^15+77988x^16+58244x^17+24568x^18+7472x^19+1640x^20+382x^21+47x^22+4x^23+1x^24+2x^26

The gray image is a code over GF(2) with n=128, k=18 and d=44.
This code was found by Heurico 1.16 in 156 seconds.