The generator matrix

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

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+366x^44+176x^45+400x^46+176x^47+469x^48+144x^49+240x^50+16x^51+54x^52+1x^56+4x^60+1x^72

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 0.11 seconds.