The generator matrix

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

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+386x^31+1113x^32+2602x^33+3805x^34+5506x^35+5764x^36+5926x^37+3930x^38+2252x^39+903x^40+424x^41+89x^42+42x^43+10x^44+6x^45+6x^47+1x^48+2x^49

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 4.97 seconds.