The generator matrix

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

generates a code of length 36 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+348x^33+744x^34+766x^35+791x^36+468x^37+482x^38+262x^39+102x^40+100x^41+21x^42+8x^43+2x^44+1x^46

The gray image is a code over GF(2) with n=288, k=12 and d=132.
This code was found by Heurico 1.16 in 0.093 seconds.