The generator matrix

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

generates a code of length 33 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+270x^30+878x^31+554x^32+1036x^33+322x^34+618x^35+205x^36+112x^37+79x^38+12x^39+8x^40+1x^42

The gray image is a code over GF(2) with n=264, k=12 and d=120.
This code was found by Heurico 1.16 in 0.078 seconds.