The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+368x^50+1786x^51+3870x^52+7134x^53+9953x^54+15132x^55+17049x^56+20190x^57+17452x^58+15548x^59+10149x^60+6776x^61+3224x^62+1524x^63+538x^64+234x^65+88x^66+26x^67+25x^68+3x^70+2x^77

The gray image is a code over GF(2) with n=456, k=17 and d=200.
This code was found by Heurico 1.16 in 123 seconds.