The generator matrix

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

generates a code of length 59 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+28x^57+10x^58+192x^59+10x^60+4x^62+3x^64+2x^66+2x^68+4x^73

The gray image is a code over GF(2) with n=472, k=8 and d=228.
This code was found by Heurico 1.16 in 1.45 seconds.