The generator matrix

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

generates a code of length 36 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+108x^30+904x^31+2728x^32+4762x^33+7395x^34+10888x^35+11822x^36+10944x^37+8026x^38+4556x^39+2159x^40+874x^41+247x^42+80x^43+24x^44+12x^45+4x^47+2x^48

The gray image is a code over GF(2) with n=288, k=16 and d=120.
This code was found by Heurico 1.16 in 17.2 seconds.