The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  2  1  1  0  1  1  0  X  1  1  1  1  1  1  1 X^2+2 X^2  X X^2  X X^2+2  1
 0  X  0  X  0  2 X^2+X  X X^2 X^2+X X^2 X^2+X+2 X^2 X^2+2 X+2 X^2+X+2 X^2 X^2+2 X^2+X+2 X^2+X+2  X X^2+2 X^2+2 X^2+X  X X^2+2 X^2+2  X  0 X^2+X+2 X^2  0 X^2+X  X  2  0  2  X  0 X^2 X^2+X+2  X  0
 0  0  X  X X^2+2 X^2+X+2 X^2+X X^2 X^2+2  2  0 X^2+2  X X^2+X X^2+X  X X+2 X^2+X  2 X^2+2 X^2  X X^2+2 X+2 X^2+X  0 X^2+X+2  0 X+2 X^2+2  0 X^2+X  X  X X^2 X^2+2  X X^2 X^2+X  X X^2+2  X X^2+X+2
 0  0  0  2  0  0  0  2  2  2  2  0  2  2  0  2  0  0  2  0  2  0  0  0  2  2  2  0  2  2  0  2  0  2  0  2  2  2  0  2  0  0  0
 0  0  0  0  2  2  0  0  0  2  2  2  0  2  2  2  2  0  0  0  2  2  2  2  0  0  0  2  0  0  0  2  0  2  0  2  0  2  2  2  2  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+82x^38+216x^39+345x^40+506x^41+704x^42+576x^43+649x^44+396x^45+275x^46+152x^47+82x^48+58x^49+24x^50+16x^51+11x^52+2x^54+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 0.234 seconds.