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  X  1  1  X  X X^2 X^2
 0 X^2+2  0 X^2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  2 X^2 X^2  2 X^2  2 X^2 X^2  0 X^2+2  2  0  2 X^2 X^2 X^2+2 X^2+2  2  2  0  2 X^2 X^2+2  2 X^2+2 X^2+2 X^2 X^2+2 X^2+2 X^2
 0  0 X^2+2 X^2  0 X^2+2 X^2  0  0 X^2+2 X^2  0  0 X^2+2 X^2  0  2 X^2  0 X^2+2  2  0 X^2+2 X^2+2  2  2 X^2+2 X^2+2  2 X^2  0 X^2+2  2 X^2  0 X^2 X^2  0  2 X^2+2  2 X^2 X^2+2 X^2  2  2 X^2+2
 0  0  0  2  0  0  2  0  2  2  0  2  2  2  0  2  2  0  2  0  0  0  2  2  0  2  0  2  0  0  2  2  0  0  2  2  0  2  2  0  2  2  2  2  0  0  0
 0  0  0  0  2  2  2  2  2  2  0  2  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  0  2  0  2  2  0  0  0  2  0  0  2  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+110x^44+96x^45+128x^46+320x^47+231x^48+96x^49+33x^52+8x^56+1x^84

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 22.8 seconds.