The generator matrix

 1  0  1  1  1 X+2  X  1  1  2  1  1  1  1 3X+2  1  1 2X  1  1  1  1 2X+2 3X  1  1  X  1  1  X  1  1  1  1  X  1  1  1  1  1 3X+2  X  1
 0  1 X+1 3X+2  3  1  1  2 3X+3  1 X+2 2X+3  X 2X+1  1 2X X+1  1 2X+2 X+3 3X  1  1  1  0 3X+2  X 2X  X 2X+2  0 3X  0 X+2 2X+2 X+1 X+3 3X+1 2X+1  3  1  1  0
 0  0 2X+2  0  2 2X+2  2  0  2  0 2X+2 2X  2 2X  0 2X+2 2X 2X+2  2 2X  0 2X+2  2  0  0 2X 2X+2  2  2 2X+2 2X+2 2X+2  0 2X 2X 2X  0 2X  0  2  0 2X+2  0
 0  0  0 2X  0  0 2X  0 2X 2X  0  0  0 2X  0 2X 2X  0 2X  0 2X 2X 2X 2X 2X  0 2X  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0  0  0  0  0
 0  0  0  0 2X  0 2X 2X  0 2X 2X 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0 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+56x^38+178x^39+305x^40+622x^41+405x^42+1008x^43+498x^44+580x^45+153x^46+136x^47+90x^48+30x^49+21x^50+2x^51+1x^52+3x^54+2x^55+2x^58+2x^59+1x^60

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 0.188 seconds.