The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+146x^29+1048x^30+3534x^31+8372x^32+17124x^33+30309x^34+45924x^35+49177x^36+45236x^37+31301x^38+17834x^39+7655x^40+3038x^41+1063x^42+256x^43+75x^44+22x^45+23x^46+4x^47+2x^49

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 270 seconds.