The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+128x^33+1064x^34+2724x^35+4399x^36+8302x^37+9761x^38+12662x^39+9985x^40+8444x^41+4414x^42+2400x^43+857x^44+256x^45+97x^46+22x^47+14x^48+4x^49+2x^53

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 20.4 seconds.