The generator matrix

 1  0  0  1  1  1  X  1 X^2  1 X^2+X X^2  1  1  1  X X^2+X  1 X^2+2 X^2+2  1  X  1 X^2+X  1  1 X^2+X+2  1  1  1 X^2+2  1 X^2+2  1  1  1  2  1  1  1  X  2  1  1  1  1 X^2+2  1  1  1
 0  1  0  0 X^2+1 X^2+X+1  1 X^2+X  1  3  1 X+2  3 X+2  2 X^2+X  1 X^2  1 X+2  3  1 X+1  X X+3 X^2+X  1  3 X^2+X+1  X  1 X^2+3  1 X^2+X+2 X^2+X+2 X+1 X^2  2  0 X^2+2  1 X+2  X X+3 X^2+X+1 X+3  0 X^2+1  X  0
 0  0  1  1  1  0 X^2+X+1  3  2 X^2+1 X^2+X+1  1 X^2+X+2 X^2+X+2  3  1 X^2+3 X^2+X X^2+X  1 X+1  2 X^2+X  1 X+1  2 X^2+3 X^2+2  1 X^2 X^2+1 X^2+2  1  3 X+2 X^2+X+1  1  2 X^2+X+3 X^2+X+2 X+3  1 X+3  0 X+3 X+1  1 X+2  3  0
 0  0  0  X X+2 X+2 X^2+X  X X+2  2  2 X^2+X+2 X^2+2 X^2+X X^2 X^2+X+2 X^2+X X+2 X^2+X+2 X^2 X^2+X+2 X^2+2  0  0 X^2+X  2 X^2+2 X^2+X X^2+2  X X^2+X  0  0  2 X+2 X^2+2 X^2+X X^2+X X+2 X^2 X+2  X X^2+2 X^2+X+2  0  2  2 X^2+X X^2+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+118x^44+710x^45+1834x^46+2792x^47+3763x^48+4912x^49+4879x^50+4848x^51+3707x^52+2614x^53+1472x^54+628x^55+278x^56+116x^57+63x^58+18x^59+5x^60+8x^62+2x^67

The gray image is a code over GF(2) with n=400, k=15 and d=176.
This code was found by Heurico 1.16 in 7 seconds.