The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0 X^2+X  2 X+2  X X^2+X+2  1
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  0 X+1  1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  0 X^2+X  2 X+2 X^2+X+2 X^2+2 X^2  X X+1 X^2+1 X+3 X^2+3 X^2+X+3 X^2+X+1  3  1  1  1  1  1  1  1  0
 0  0  2  0  2  0  2  0  2  2  0  2  0  0  0  2  0  0  2  2  2  0  2  2  2  0  2  0  2  0  0  2  0  0  2  2  0  2  0  2  2  2  2  0  0  2  0
 0  0  0  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  2  2  0  0  0  2  0  0  2  0  0  2  2  0  2  2  0  2  0  0  2  2  0  0  0  2  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+27x^44+344x^45+35x^46+208x^47+35x^48+344x^49+27x^50+1x^60+1x^62+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 0.062 seconds.