The generator matrix

 1  0  0  1  1  1 2X+2 2X+2  1  2  1 3X  1  1 3X+2  1 3X+2  1  1 2X+2 2X+2  1  1 2X+2 2X+2 3X+2 X+2  1 3X  1 3X  1 2X+2 X+2  1  1
 0  1  0  X 2X+1 X+1  1  X 3X+2  1 X+1  1  X X+3  1 X+2 3X+2  1  2  1  X 2X 3X+1  1  1 2X  1  3  1 2X+1  1 X+3  1 3X X+2 2X
 0  0  1  1  1  0  1  1 X+2 3X 3X+1  3 X+3  X X+1 2X  1 3X X+3 X+1  1 X+2 3X+1 3X  3  1 3X+3  2  2 X+2 2X+3  3 2X+2  1 2X+1  0
 0  0  0  2 2X+2 2X  2 2X+2 2X+2 2X+2  0  0  0 2X  2  0  2  2 2X 2X  0  2  2  0 2X 2X 2X+2 2X+2 2X 2X 2X+2  0 2X+2 2X+2  0  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+74x^31+597x^32+1330x^33+2098x^34+2594x^35+3176x^36+2606x^37+1941x^38+1210x^39+556x^40+82x^41+64x^42+26x^43+12x^44+14x^45+1x^46+2x^48

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 1.28 seconds.