The generator matrix

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

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+52x^38+270x^39+240x^40+640x^41+488x^42+866x^43+496x^44+498x^45+185x^46+198x^47+44x^48+72x^49+25x^50+10x^51+2x^52+6x^53+1x^54+1x^56+1x^66

The gray image is a code over GF(2) with n=344, k=12 and d=152.
This code was found by Heurico 1.16 in 0.235 seconds.