The generator matrix

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

generates a code of length 47 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+124x^43+178x^44+168x^45+336x^46+456x^47+402x^48+160x^49+48x^50+92x^51+46x^52+24x^53+12x^56+1x^80

The gray image is a code over GF(2) with n=376, k=11 and d=172.
This code was found by Heurico 1.16 in 35.1 seconds.