The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+352x^11+1730x^12+7822x^13+24503x^14+57388x^15+78084x^16+58116x^17+24568x^18+7520x^19+1624x^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 137 seconds.