The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+248x^32+1334x^33+3959x^34+9406x^35+17911x^36+31222x^37+42278x^38+48322x^39+43375x^40+32174x^41+17739x^42+8760x^43+3630x^44+1250x^45+368x^46+114x^47+18x^48+20x^49+8x^50+6x^51+1x^52

The gray image is a code over GF(2) with n=312, k=18 and d=128.
This code was found by Heurico 1.16 in 296 seconds.