The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  2  X X^2  X  0  X  X X^2+2  X  X  X  0  X  0  X  X  X  2 X^2  2 X^2  X X^2  X  X  X
 0  X  0 X^2+X+2  0 X^2+X  0 X+2 X^2 X^2+X X^2+2  X X^2 X^2+X+2 X^2+2 X+2  2 X^2+X  2  X  2 X^2+X+2  2 X+2 X^2+2 X^2+X+2 X^2 X+2 X^2+2 X^2+X X^2  X X^2+X  X X+2  X X^2+X+2  X X^2  X  X X^2+2  2 X^2+X+2  X X^2+X+2  X X^2+X X^2+X X+2  X  0  X  X  0  X  2 X^2+2 X+2
 0  0 X^2+2 X^2  2 X^2+2 X^2  2 X^2  0  0 X^2 X^2+2  2  2 X^2+2  2  2 X^2 X^2+2  0  0 X^2+2 X^2 X^2+2 X^2+2  2  0 X^2 X^2  0  2  0 X^2  2 X^2+2 X^2  0 X^2+2 X^2  2 X^2+2 X^2  0 X^2 X^2+2  2 X^2  2 X^2+2 X^2+2 X^2+2  0  0  0 X^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+148x^57+68x^58+124x^59+40x^60+76x^61+12x^62+36x^63+5x^64+2x^72

The gray image is a code over GF(2) with n=472, k=9 and d=228.
This code was found by Heurico 1.16 in 0.438 seconds.