The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+242x^49+1496x^50+3286x^51+7546x^52+12338x^53+20509x^54+28668x^55+36758x^56+39858x^57+37023x^58+29092x^59+21503x^60+12198x^61+6762x^62+2810x^63+1299x^64+448x^65+183x^66+62x^67+29x^68+18x^69+11x^70+2x^77+2x^79

The gray image is a code over GF(2) with n=456, k=18 and d=196.
This code was found by Heurico 1.16 in 480 seconds.