The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+327x^36+1764x^37+5072x^38+9896x^39+19660x^40+29816x^41+41644x^42+44852x^43+42717x^44+30260x^45+19748x^46+9712x^47+4362x^48+1584x^49+502x^50+116x^51+100x^52+8x^54+1x^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 337 seconds.