The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  0  1  1 X+2  1  1  1  0  2  1  1 X+2  1  1 X+2  1  1  1  0  1  1  1 X+2  0  1 X+2  1  1  1  X  1  1 X+2  0  1  0  1  1  1  1  X  1  1  1  1
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  1  0  3  1 X+2 X+1  X  1  1 X+1  0  1  3  2  1 X+2  3 X+1  1  0 X+2 X+1  1  1 X+1  1 X+2  3 X+1  1  0  3  1  1 X+2  1  3 X+3  0 X+1  1  0  3 X+3  3
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  2  2  2  0  2  2  0  2  0  0  2  2  0  2  0  2  2  2  2  0  0  2  0  2  2  0  0  2  2  0  0  0  2  2  2  0  2  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  2  0  2  2  2  2  0  2  0  2  2  0  2  0  2  2  0  2  0  0  0  2  0  0  2  0  0  2  2  0  0  0  2  2  0  2  0  2  2  2  0  0
 0  0  0  0  2  0  0  0  0  0  0  2  2  0  2  2  2  2  2  0  2  2  0  0  0  0  2  2  2  2  0  2  0  0  0  0  0  2  2  0  0  0  0  2  0  2  0  2  2  2  0  2  2  2  2  2  2
 0  0  0  0  0  2  0  0  0  0  2  2  2  0  2  0  0  2  0  2  0  0  2  2  0  2  0  0  0  2  2  2  0  0  0  2  2  0  0  0  2  0  2  0  2  2  2  2  2  2  2  2  2  0  2  2  0
 0  0  0  0  0  0  2  0  0  2  2  0  0  2  2  0  0  2  2  2  2  2  0  0  0  2  2  0  2  0  0  2  2  0  0  2  0  0  0  2  2  2  0  2  0  0  2  2  2  2  0  0  0  2  0  0  2
 0  0  0  0  0  0  0  2  0  2  0  0  0  0  0  0  2  2  0  0  0  2  2  2  2  2  2  0  0  2  2  2  0  2  0  0  0  0  2  2  2  0  2  2  2  2  0  2  0  0  0  2  0  0  2  0  0
 0  0  0  0  0  0  0  0  2  0  2  2  0  0  2  2  2  2  2  0  0  0  0  2  2  0  2  0  0  0  2  0  2  2  2  0  2  2  0  2  0  0  0  0  2  0  2  2  0  2  2  0  2  2  2  0  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+127x^48+20x^49+184x^50+160x^51+530x^52+368x^53+700x^54+608x^55+1080x^56+760x^57+972x^58+608x^59+770x^60+368x^61+404x^62+160x^63+239x^64+20x^65+44x^66+34x^68+24x^72+10x^76+1x^80

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 3.57 seconds.