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

generates a code of length 58 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+20x^55+130x^56+96x^57+512x^58+136x^59+120x^60+4x^63+4x^64+1x^112

The gray image is a code over GF(2) with n=464, k=10 and d=220.
This code was found by Heurico 1.16 in 0.265 seconds.