The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1
 0  X  0 X^2+X X^2 X^2+X+2 X^2+2  X  0 X^2+X X^2+2 X+2  2  X X^2+2 X^2+X+2  X  0 X^2+2 X^2+X X^2+X  2 X^2 X+2 X+2  0 X^2+X X^2+X  0 X^2+2 X^2+2 X+2 X+2  2  2  2 X^2+X X^2+X+2 X^2+X+2 X^2 X^2 X^2  0 X^2+X  X  2 X^2
 0  0 X^2+2  0 X^2+2 X^2  0 X^2  2  2  2  2 X^2 X^2+2 X^2 X^2+2 X^2  0  0  0 X^2 X^2 X^2+2  0 X^2+2  2 X^2+2  2 X^2+2 X^2  2  2 X^2+2  2 X^2+2  0 X^2  2  0  2 X^2  0 X^2  0  0 X^2+2  2
 0  0  0  2  2  0  2  2  0  2  2  0  0  2  2  0  0  2  0  0  2  2  0  2  0  2  2  0  2  0  0  2  2  0  2  2  0  0  2  2  0  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+72x^44+42x^45+247x^46+304x^47+247x^48+36x^49+71x^50+2x^53+1x^54+1x^90

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 0.109 seconds.