The generator matrix

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

generates a code of length 59 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+12x^57+31x^58+170x^59+28x^60+8x^61+1x^62+2x^63+2x^76+1x^84

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 0.125 seconds.