The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+257x^32+1250x^33+4208x^34+9154x^35+18369x^36+30318x^37+42927x^38+47712x^39+44376x^40+31264x^41+18488x^42+8568x^43+3465x^44+1118x^45+473x^46+144x^47+28x^48+2x^49+14x^50+6x^51+2x^54

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 293 seconds.