The generator matrix

 1  0  0  0  1  1  1  2  1  1  1  1 X^2+X+2  X  X X+2  X  1  1 X^2+X  1 X^2+X+2  1 X+2  1  1  1  0  1 X^2  1  1  0 X^2+X+2 X+2  1  1 X^2  1  1  1  1  2  1 X^2  X X^2  1  X  1
 0  1  0  0  2  1  3  1 X^2+2  2 X+3 X^2+X+3  1  1 X^2+X  1 X^2  3 X^2+X  1 X^2+X  2  X X^2+X X^2+X+2 X+1 X^2+X+1  1 X+2  1 X+2 X+1  X X+2  1 X^2 X^2+3 X+2 X^2+2  3 X^2+1 X^2+3  1  X  2  1  1 X^2+X+2  X  2
 0  0  1  0  3  1  2  3  0 X^2+X+1 X+1 X^2 X^2 X^2+X+1  1 X+2  1 X+3 X^2+3 X^2+X+1 X^2+X  1 X^2+X+1 X+2  0  3  0 X+2 X^2+2 X^2+X+2 X^2+X+1 X+2  1  1 X^2+2 X^2+X+2 X+3 X^2+X+2  X X^2+1  2 X^2+X+3 X+1 X^2+1  1 X^2+1 X+2 X+3  2  0
 0  0  0  1  1  2  3  3 X^2+1 X^2+X  1  X  1 X^2+X+2 X^2+X+1 X^2+X+1 X^2+1 X+1 X^2+X X^2+2 X+2 X^2+2  3  1 X^2+X+3  0 X+3 X^2  2 X+1 X+1 X^2+2 X^2+X+2 X^2+X X^2  3  2  1 X^2+X+1 X+3  X X^2+1 X+1  2 X+1 X^2+2 X^2+3 X^2+X  1 X^2

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+466x^44+1586x^45+3480x^46+5300x^47+7529x^48+9218x^49+10440x^50+9480x^51+7634x^52+5134x^53+3040x^54+1324x^55+596x^56+190x^57+64x^58+24x^59+28x^60+2x^64

The gray image is a code over GF(2) with n=400, k=16 and d=176.
This code was found by Heurico 1.16 in 25.9 seconds.