The generator matrix

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

generates a code of length 47 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+238x^44+366x^45+371x^46+306x^47+239x^48+214x^49+175x^50+70x^51+53x^52+4x^53+5x^54+4x^56+1x^60+1x^66

The gray image is a code over GF(2) with n=376, k=11 and d=176.
This code was found by Heurico 1.16 in 0.078 seconds.