The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  0  1  1 X^2+X  1 X^2+X X^2+2  1  1  1  1  1  1  1  1  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  0 X+1  1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1 X+2  1 X+1 X^2+1  1  0  1  1 X^2+1  0 X^2+X X^2+3 X^2+X+3 X^2+1 X+1 X+1 X+3 X^2+X+3 X^2+1
 0  0  2  0  0  0  0  2  0  2  2  2  0  0  0  2  2  2  0  0  0  2  2  2  0  2  0  0  2  2  0  2  0  2  2  2  0  2  0  2  2  0  0
 0  0  0  2  0  0  2  2  0  2  0  2  0  2  2  2  0  0  0  0  2  0  0  2  0  2  2  2  2  2  0  0  2  2  0  2  2  2  2  2  2  0  2
 0  0  0  0  2  0  2  0  2  2  2  2  0  2  0  0  2  0  2  0  0  2  0  0  0  2  2  2  2  0  2  2  0  2  2  0  0  0  0  0  2  0  2
 0  0  0  0  0  2  0  2  2  2  0  2  2  0  2  0  2  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  0  2  0  0  2  2  0  0  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+72x^38+200x^39+221x^40+608x^41+480x^42+944x^43+480x^44+608x^45+210x^46+200x^47+63x^48+4x^54+3x^56+2x^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 0.156 seconds.