The generator matrix

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

generates a code of length 36 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+142x^29+960x^30+3702x^31+7923x^32+18008x^33+30643x^34+43774x^35+50785x^36+44954x^37+31182x^38+18032x^39+7540x^40+3100x^41+951x^42+360x^43+49x^44+20x^45+8x^46+2x^47+6x^48+2x^51

The gray image is a code over GF(2) with n=288, k=18 and d=116.
This code was found by Heurico 1.16 in 278 seconds.