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

generates a code of length 50 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+81x^44+82x^46+32x^47+171x^48+608x^49+126x^50+608x^51+149x^52+32x^53+94x^54+31x^56+18x^58+9x^60+4x^64+1x^72+1x^84

The gray image is a code over GF(2) with n=400, k=11 and d=176.
This code was found by Heurico 1.16 in 0.187 seconds.