The generator matrix

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

generates a code of length 43 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+224x^39+323x^40+530x^41+701x^42+598x^43+734x^44+456x^45+258x^46+214x^47+21x^48+18x^49+1x^50+2x^51+7x^52+4x^53+2x^55+1x^56+1x^60

The gray image is a code over GF(2) with n=344, k=12 and d=156.
This code was found by Heurico 1.16 in 149 seconds.