The generator matrix

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

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+428x^31+1051x^32+2816x^33+3650x^34+5704x^35+5485x^36+5884x^37+3700x^38+2596x^39+855x^40+416x^41+74x^42+72x^43+27x^44+4x^45+5x^48

The gray image is a code over GF(2) with n=288, k=15 and d=124.
This code was found by Heurico 1.16 in 7.52 seconds.