The generator matrix

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

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+44x^50+102x^51+139x^52+116x^53+139x^54+200x^55+207x^56+218x^57+222x^58+210x^59+113x^60+82x^61+77x^62+46x^63+36x^64+30x^65+25x^66+16x^67+16x^68+2x^69+4x^70+2x^71+1x^90

The gray image is a code over GF(2) with n=228, k=11 and d=100.
This code was found by Heurico 1.16 in 0.349 seconds.