The generator matrix

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

generates a code of length 43 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+164x^37+1379x^38+2812x^39+5408x^40+7198x^41+10266x^42+10634x^43+11075x^44+7434x^45+5079x^46+2362x^47+1201x^48+338x^49+134x^50+30x^51+11x^52+2x^53+4x^54+2x^55+2x^58

The gray image is a code over GF(2) with n=344, k=16 and d=148.
This code was found by Heurico 1.16 in 21 seconds.