The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+48x^48+100x^49+145x^50+360x^51+316x^52+622x^53+495x^54+912x^55+578x^56+1144x^57+562x^58+952x^59+449x^60+604x^61+258x^62+296x^63+111x^64+84x^65+57x^66+32x^67+26x^68+6x^69+15x^70+8x^71+6x^72+4x^74+1x^76

The gray image is a code over GF(2) with n=228, k=13 and d=96.
This code was found by Heurico 1.16 in 3.46 seconds.