The generator matrix

 1  0  0  1  1  1  X  1 X^2+2  1 X+2  1  1  X  1  0  1  1 X^2  1  1  1  1 X^2+X  1  X X^2+2  1 X^2+X+2  1  0 X^2+2 X^2+2  1  1  1  1  2  1  1  X  1  2 X^2+2  1  1  1
 0  1  0  0 X^2+1 X^2+X+1  1 X^2+X  1  X  1  3 X^2+X+3 X^2 X+1  X X^2+X+1  2  1  0 X^2+1  1 X^2+X  1 X^2+X  1 X^2 X+3  1 X^2+3  1 X^2  1  3  X X^2+2 X^2+X  1 X^2 X+2  1 X^2+X+1  1  X  X  X  0
 0  0  1  1  1  0 X^2+X+1 X^2+3  2  0 X^2+1 X^2  1  1 X^2+X+1  1 X+2 X^2+X+1 X^2+X+2  X X^2+X+1 X^2+X X^2+X+2 X^2+X+3 X+2  0  1  X X+3 X^2+X+3 X+2  1  X X^2+2 X+3 X^2+X+1 X+1 X^2+X+1  X X+1 X^2+X X+1 X^2+X+3  1 X^2+1 X^2+X+2 X^2+2
 0  0  0  X X+2 X+2 X^2+X  0 X+2 X^2+X+2  2 X^2+2 X^2 X^2+X+2 X^2  X  0  X X^2+X+2  2 X^2+X  2  X X^2+2 X^2+2 X+2 X^2 X+2  2 X^2 X^2+2 X+2  2  X X^2  2 X^2+X+2  2 X^2+X+2  0  0 X+2 X+2 X^2+X X^2+2  2 X^2+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+108x^41+841x^42+1428x^43+2750x^44+3718x^45+5072x^46+4934x^47+5341x^48+3704x^49+2598x^50+1232x^51+640x^52+214x^53+128x^54+22x^55+34x^56+1x^58+2x^60

The gray image is a code over GF(2) with n=376, k=15 and d=164.
This code was found by Heurico 1.16 in 6.45 seconds.