The generator matrix

 1  0  0  0  1  1  1  2  1  1 X^2+X+2 X^2+X+2 X^2+X  1  1  1  1  1  1  1 X^2 X^2+X+2  0  1  1  0  1 X^2+2  1  1  0  2  X X^2+2  1  1  1 X^2 X^2+X  1  1 X^2+X  1 X+2  1  0  1
 0  1  0  0  2  1  3  1 X^2+X+2 X^2+X X^2+X+2  1  1 X^2+3 X+3 X+2 X^2+X+1 X^2+X X^2+1 X^2+X+1  1 X+2  1 X^2+X+2 X+2  1 X+3  1 X^2+2 X^2+X+3  1 X^2+X X^2+X+2  1 X^2+1 X+2 X^2+X  1  1 X+3 X^2  1  0  1 X^2+X+2 X^2+X X^2
 0  0  1  0  3  1  2  3  0  1  1 X^2+1 X^2+2 X+2 X^2+X+3  X X^2+X X+1 X^2+1 X^2 X^2+X+3  1  X  3  0 X+3 X^2+1 X^2 X^2+2 X^2+1 X^2+1 X^2+X  1  X X^2+X+1  2  X X^2+X+2  2  3 X^2+3  1 X^2+X+1  X X+3  1 X^2+2
 0  0  0  1  1  2  3  3 X^2+X+1  X  3 X^2+X+2 X+3 X^2+X+2 X+1 X^2+1 X+3 X^2+1 X+3 X^2+X  3  2 X^2+2 X^2+2 X^2+X X^2+X X^2+X X^2+X+3 X+3  3 X^2+X+1  1  X X+2 X^2  0 X+3 X+3 X^2+2  0 X^2+X+3  0 X^2+X+3 X^2+X+1  1 X^2+X+1  2

generates a code of length 47 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+266x^41+1536x^42+3234x^43+5515x^44+7134x^45+9999x^46+10170x^47+10206x^48+7444x^49+5173x^50+2838x^51+1429x^52+334x^53+163x^54+62x^55+17x^56+6x^57+7x^58+2x^62

The gray image is a code over GF(2) with n=376, k=16 and d=164.
This code was found by Heurico 1.16 in 24.6 seconds.