The generator matrix

 1  0  1  1  1 X^2+X+2  1  1 X^2+2  1  1  2  1  1  X  1  1  1  1  X  1  1 X^2 X^2+X X^2+2 X+2  2 X^2+X  2  X X^2+X+2  2  1  1  1  1  1  1  1  1  1  2 X^2+X  1  1 X^2  1 X^2  1  1  1  1  1  1 X^2+X+2  X  X  1
 0  1 X+1 X^2+X+2 X^2+1  1  2 X^2+X+1  1 X^2+2 X+1  1  X  3  1 X^2 X^2+3 X^2+X X^2+X+3  1 X+2  1  1  1  1  1  1  1  1  1  1  1  0 X^2+X X^2+X  0 X^2+2  X  0 X^2+2  X  X  1 X^2+2 X+2  1  3  1 X^2+2 X^2 X^2+X X+1  X X+2  1  X X+2  0
 0  0 X^2 X^2  2 X^2 X^2+2 X^2+2  2  2  0 X^2+2 X^2  2 X^2 X^2+2 X^2  0  0 X^2  2 X^2+2 X^2+2  0  0  2 X^2  2  2  0 X^2+2 X^2+2  2  0 X^2 X^2  0 X^2+2  0 X^2+2  0  2 X^2+2 X^2  2  2  0 X^2 X^2  2  2  2 X^2 X^2+2  0 X^2 X^2+2  2
 0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  2  2  2  0  0  0  0  2  0  2  0  0  2  0  2  2  0  2  0  0  2  0  2  2  0  2  2  0  0  2  0  0  0  2  0  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 54.

Homogenous weight enumerator: w(x)=1x^0+59x^54+356x^55+224x^56+294x^57+227x^58+296x^59+172x^60+308x^61+80x^62+20x^63+1x^64+6x^65+1x^70+2x^72+1x^90

The gray image is a code over GF(2) with n=464, k=11 and d=216.
This code was found by Heurico 1.16 in 0.203 seconds.