The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X X^2+2  1  1  1  1  X  1  1  1  1  1  0  1  X  1  2  1  X  X  1 X^2  1 X^2 X^2
 0  X  0 X^2+X+2 X^2 X^2+X X^2+2  X  2  0 X^2+X X^2+X X^2 X^2 X+2  X X^2+X  X X+2  X  0 X^2 X^2+X+2  X X^2+X+2 X+2 X^2+X  2 X^2+X  X  X  0 X^2+X+2  X  X X^2+X  0 X^2+X+2 X^2+X+2  X X^2+X  2 X^2
 0  0 X^2+2  0 X^2  0  0  2  0 X^2 X^2 X^2 X^2  2 X^2+2 X^2 X^2+2  2 X^2  2  0  2  0  0 X^2+2  0 X^2 X^2 X^2 X^2+2 X^2 X^2  0  2  0  2 X^2+2  0  2  2 X^2+2 X^2+2  2
 0  0  0 X^2+2  0  0  2 X^2 X^2 X^2 X^2  2 X^2+2 X^2  0 X^2 X^2+2  0 X^2+2  2  2 X^2+2 X^2  2  0  2 X^2  0  0 X^2+2 X^2  2 X^2+2 X^2 X^2 X^2 X^2+2 X^2  0 X^2  0 X^2 X^2+2
 0  0  0  0  2  2  2  2  0  0  0  2  2  2  0  2  0  0  0  0  0  2  0  0  2  2  2  2  0  0  2  2  0  0  2  2  2  2  2  0  0  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+225x^38+40x^39+520x^40+272x^41+850x^42+416x^43+736x^44+240x^45+547x^46+56x^47+132x^48+33x^50+11x^52+8x^54+7x^56+1x^58+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 0.437 seconds.