The generator matrix

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

generates a code of length 36 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+63x^32+448x^33+545x^34+690x^35+716x^36+722x^37+415x^38+320x^39+90x^40+36x^41+13x^42+22x^43+10x^44+2x^45+3x^46

The gray image is a code over GF(2) with n=288, k=12 and d=128.
This code was found by Heurico 1.16 in 0.125 seconds.