The generator matrix

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

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+142x^37+726x^38+1450x^39+2671x^40+3828x^41+4878x^42+5328x^43+5173x^44+3936x^45+2428x^46+1170x^47+636x^48+236x^49+110x^50+28x^51+15x^52+2x^53+2x^54+8x^55

The gray image is a code over GF(2) with n=344, k=15 and d=148.
This code was found by Heurico 1.16 in 6.41 seconds.