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

generates a code of length 58 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+112x^53+9x^54+132x^55+128x^56+276x^57+751x^58+264x^59+124x^60+120x^61+7x^62+116x^63+2x^64+4x^65+1x^66+1x^112

The gray image is a code over GF(2) with n=464, k=11 and d=212.
This code was found by Heurico 1.16 in 0.282 seconds.