The generator matrix

 1  0  1  1  1 X^2+X+2  1  1  0  1 X^2+X+2  1  1  1  1  2  1 X+2  1  1  0  1 X+2  1  1  1  1  1 X^2+2  1  X  1 X^2  1 X^2+X+2  1  1  1  1  1 X^2 X^2+X+2  1  1  0  1  1  1  1  1  X  1 X^2+2  1  1  1  1  1
 0  1 X+1 X^2+X+2 X^2+1  1 X^2+3  0  1 X^2+X+2  1 X+1  3 X^2+X+1  2  1 X+2  1 X^2+X+3  0  1 X+2  1  1 X^2+X+3 X^2+3 X+1 X^2  1 X^2+X+1  1 X^2  1  1  1  X X^2+X+1  1 X+3  X  X  1 X+1  3  1  3 X+2  3 X^2+X X+2 X+2 X^2+1  1  3 X^2+X+3 X^2+X+1 X+2  0
 0  0 X^2  0  0  0  0 X^2 X^2+2 X^2+2 X^2 X^2+2  2 X^2 X^2+2 X^2  2  2 X^2  2  2 X^2 X^2+2  2 X^2+2 X^2  0  0 X^2  2 X^2+2  2  2 X^2  0 X^2  2 X^2  2 X^2  0 X^2+2  0 X^2+2  0 X^2+2 X^2+2  2  0  0  2 X^2+2  2 X^2+2  0  0 X^2+2  0
 0  0  0 X^2+2  2 X^2+2 X^2 X^2 X^2+2  2  0 X^2+2  0  2  0  2  2  2 X^2+2 X^2+2 X^2+2 X^2 X^2+2 X^2 X^2  0  2 X^2+2 X^2 X^2  0  2 X^2 X^2+2  2  0  2  2 X^2+2 X^2+2 X^2+2  2  0 X^2  2 X^2+2  0 X^2+2  2 X^2 X^2+2  0  2  0 X^2+2 X^2 X^2+2  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+54x^53+245x^54+462x^55+525x^56+544x^57+544x^58+496x^59+528x^60+396x^61+132x^62+82x^63+62x^64+12x^65+5x^66+2x^68+2x^69+2x^72+1x^78+1x^82

The gray image is a code over GF(2) with n=464, k=12 and d=212.
This code was found by Heurico 1.16 in 0.297 seconds.