The generator matrix

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

generates a code of length 36 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+850x^31+2360x^32+5042x^33+7464x^34+10914x^35+12086x^36+11146x^37+7982x^38+4794x^39+1741x^40+842x^41+220x^42+66x^43+12x^44+10x^45+6x^46

The gray image is a code over GF(2) with n=288, k=16 and d=124.
This code was found by Heurico 1.16 in 195 seconds.