The generator matrix

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

generates a code of length 40 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+328x^33+1402x^34+4060x^35+9586x^36+19018x^37+29480x^38+43638x^39+46374x^40+43836x^41+30980x^42+19016x^43+8804x^44+3724x^45+1224x^46+480x^47+129x^48+36x^49+18x^50+4x^51+2x^52+2x^53+2x^55

The gray image is a code over GF(2) with n=320, k=18 and d=132.
This code was found by Heurico 1.16 in 296 seconds.