The generator matrix

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

generates a code of length 43 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+451x^36+1540x^37+5424x^38+9816x^39+18991x^40+29956x^41+41824x^42+45336x^43+42577x^44+30196x^45+19784x^46+9576x^47+4364x^48+1468x^49+626x^50+104x^51+76x^52+8x^53+20x^54+4x^56+2x^58

The gray image is a code over GF(2) with n=344, k=18 and d=144.
This code was found by Heurico 1.16 in 340 seconds.