The generator matrix

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

generates a code of length 43 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+24x^38+196x^39+416x^40+504x^41+697x^42+554x^43+607x^44+480x^45+373x^46+154x^47+41x^48+24x^49+7x^50+6x^51+5x^52+2x^55+2x^58+2x^60+1x^62

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 0.172 seconds.