The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+177x^50+308x^51+521x^52+576x^53+645x^54+772x^55+785x^56+868x^57+747x^58+736x^59+561x^60+520x^61+403x^62+212x^63+144x^64+84x^65+64x^66+20x^67+26x^68+12x^70+10x^72

The gray image is a code over GF(2) with n=228, k=13 and d=100.
This code was found by Heurico 1.16 in 3.32 seconds.