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

generates a code of length 58 over Z4[X]/(X^3+2,2X) 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 0.157 seconds.