The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+116x^44+820x^45+1708x^46+2796x^47+3614x^48+4984x^49+4858x^50+5324x^51+3407x^52+2492x^53+1472x^54+716x^55+218x^56+120x^57+78x^58+28x^59+11x^60+4x^62+1x^64

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 7.74 seconds.