The generator matrix

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

generates a code of length 43 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+180x^38+842x^39+1234x^40+2186x^41+2429x^42+2908x^43+2428x^44+2062x^45+937x^46+726x^47+307x^48+86x^49+19x^50+18x^51+12x^52+2x^53+3x^54+2x^56+2x^59

The gray image is a code over GF(2) with n=344, k=14 and d=152.
This code was found by Heurico 1.16 in 1.69 seconds.