The generator matrix

 1  0  0  1  1  1  2  0  1 X^2+2 X^2+2  1  1  1 X^2+X+2 X+2  1 X+2  1  X X^2+X  1  1  1 X+2  1  1  1  1  1  X X^2+X  1 X^2+2  1  2  1  1  0  1 X^2+2  0 X+2  1 X^2+2  0  1
 0  1  0  0 X^2+1 X^2+1  1 X^2+X  2  1  1 X^2+3  1 X^2+2  X X^2 X^2+X+2  1 X+3  1  1 X^2+X+2 X^2+X+3 X+1  1  2 X^2+X+1 X^2+X+3  X X^2+3  1  1  1  1 X^2+2  1  1 X+2 X^2+X+2 X+3  1  1  1 X+1  2 X+2  2
 0  0  1 X+1 X+3  2 X^2+X+3  1 X^2+X+2 X^2+X+2  3  3  X X^2+1  1  1 X+3 X^2+1 X^2+2 X^2 X^2+X X^2 X^2+X+2 X+1 X+1 X+2  3 X^2  1 X^2+1  0 X^2+3 X^2+X+1  2  1 X+3 X^2 X^2+X  1  1 X^2+X+2 X^2+1 X^2+X+3 X^2+1  1  1  2
 0  0  0  2  2  0  2  2  2  2  0  0  2  0  2  0  0  2  2  0  2  2  0  0  2  0  0  0  0  2  2  0  0  2  2  0  2  2  0  2  0  2  0  0  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+310x^43+890x^44+1200x^45+1349x^46+1296x^47+1119x^48+798x^49+569x^50+302x^51+196x^52+96x^53+33x^54+20x^55+2x^56+10x^57+1x^58

The gray image is a code over GF(2) with n=376, k=13 and d=172.
This code was found by Heurico 1.16 in 0.453 seconds.