The generator matrix

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

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+68x^36+780x^37+2534x^38+5666x^39+9192x^40+15460x^41+19961x^42+23196x^43+20552x^44+15892x^45+9408x^46+5118x^47+2045x^48+854x^49+222x^50+96x^51+12x^52+4x^53+2x^54+4x^55+2x^56+2x^57+1x^58

The gray image is a code over GF(2) with n=344, k=17 and d=144.
This code was found by Heurico 1.16 in 85.3 seconds.