The generator matrix

 1  0  1  1  1 X^2+X+2  1  1  X  1  1 X^2+2  1  1  2  1  1 X^2+X  1  1 X^2  1  1 X+2  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  0 X^2+X X^2+2  2  1
 0  1 X+1 X^2+X+2 X^2+1  1  X X^2+X+1  1 X^2+2  3  1  2 X+1  1 X^2+X X^2+3  1 X+2 X^2+X+3  1 X^2  1  1 X^2  2 X^2+X+2  2  X X^2+2 X+2 X^2+2 X^2+X X+1 X+3 X^2+1 X^2+1 X^2+X+3 X^2+X+3  3  3  1  1  1  1  1  0
 0  0 X^2 X^2+2  2 X^2 X^2 X^2+2 X^2+2  2  0  2 X^2  0 X^2  0 X^2  0  2  2 X^2+2 X^2+2 X^2+2  2 X^2 X^2+2  2  2 X^2+2 X^2  0  0 X^2  2 X^2+2  0 X^2+2 X^2  0 X^2  2  2 X^2+2  2  0  0  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+33x^44+260x^45+169x^46+134x^47+140x^48+232x^49+29x^50+14x^51+9x^52+1x^58+1x^60+1x^66

The gray image is a code over GF(2) with n=376, k=10 and d=176.
This code was found by Heurico 1.16 in 0.063 seconds.