The generator matrix

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

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+124x^31+215x^32+318x^33+511x^34+596x^35+686x^36+594x^37+407x^38+284x^39+166x^40+106x^41+37x^42+20x^43+18x^44+6x^45+5x^46+2x^48

The gray image is a code over GF(2) with n=288, k=12 and d=124.
This code was found by Heurico 1.16 in 26.3 seconds.