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  1  1  1  1  1  1  X  X  1  1  X  X  0  2  1  1  X  1  X  1  X  1  X  1  X
 0  X  0  X  0  0  X X+2  0  2  X X+2  0 X+2  2 X+2  X  0  2  X  2 X+2  0 X+2  0  2  2  X  X  0  X  X  0  2  X  0  X  2  0  0  X X+2 X+2  X  X  X  2  2 X+2  2  0  0  0  X  X  2 X+2
 0  0  X  X  0 X+2  X  0  2  X  X  0  2 X+2  X  2  X  0 X+2  0  0  2 X+2  X  0  0  X  X  2 X+2 X+2  2  0  X  X  2 X+2  0  0 X+2  2  X  0  X  2  X  X  2  2  X X+2  0 X+2  0 X+2  2  0
 0  0  0  2  0  0  0  2  2  2  0  0  2  2  0  0  0  2  2  2  2  0  0  0  2  2  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  0  2  2  0  2  2  0  2  2  0  0  2  0  2  2
 0  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  0  2  2  2  0  2  2  2  2  0  0  2  0  2  0  2  0  0  2  2  0  0  0  2  0  0  2  0  2  2  0  0  0  2  2  0  0  0  2  0  2
 0  0  0  0  0  2  0  0  0  2  2  2  2  0  0  0  2  0  2  0  2  2  2  0  0  0  2  0  0  2  0  0  0  0  2  2  2  2  2  2  2  0  0  0  0  2  2  2  0  0  0  2  2  2  0  0  0
 0  0  0  0  0  0  2  2  2  2  2  0  2  0  0  0  2  2  2  2  2  0  0  2  0  0  2  0  2  2  0  2  2  2  2  0  0  2  0  2  2  2  2  0  0  2  0  0  2  2  0  0  2  2  2  0  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+114x^50+4x^51+174x^52+24x^53+237x^54+124x^55+277x^56+208x^57+268x^58+124x^59+216x^60+24x^61+97x^62+4x^63+78x^64+45x^66+21x^68+6x^70+1x^74+1x^92

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 0.371 seconds.