The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+114x^31+550x^32+1292x^33+2009x^34+2832x^35+2977x^36+2918x^37+1790x^38+1102x^39+509x^40+140x^41+81x^42+48x^43+19x^44+2x^45

The gray image is a code over GF(2) with n=288, k=14 and d=124.
This code was found by Heurico 1.16 in 1.36 seconds.