The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+104x^33+950x^34+2730x^35+4912x^36+7724x^37+10643x^38+11420x^39+10741x^40+7880x^41+4820x^42+2388x^43+890x^44+228x^45+51x^46+36x^47+12x^48+2x^51+4x^52

The gray image is a code over GF(2) with n=312, k=16 and d=132.
This code was found by Heurico 1.16 in 18.3 seconds.