The generator matrix

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

generates a code of length 58 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+28x^57+69x^58+8x^59+2x^60+12x^61+6x^62+1x^64+1x^66

The gray image is a code over GF(2) with n=464, k=7 and d=228.
This code was found by Heurico 1.16 in 0.156 seconds.