The generator matrix

 1  0  0  1  1  1  2  0  1  1  2 X^2  1  1 X^2+X+2  1  1 X^2+X+2  X  1  1  1  X  1  1 X+2 X^2+X  1 X+2 X^2+2  1  1  1 X^2  1 X^2+X+2  1  X  1  1  0  1  1  1 X^2+X  1  1  1  1  1  0  1  1 X+2  1  1  1 X+2
 0  1  0  0 X^2+1 X^2+1  1 X^2+X  2 X^2+3  1  1 X^2+2  3 X+2 X+1  X  1  1 X+2 X^2+X X^2+X+3 X^2 X+1 X^2+X  1  1  1 X+2  1 X+3 X^2 X^2+X+1  1 X+2  1 X^2  2  2 X^2+X+2  1  0 X+1 X^2  1  3 X^2+X+1 X+1  X  3  2 X^2+1 X^2+X+1  1 X^2+X+3 X^2+1 X^2+3 X^2+2
 0  0  1 X+1 X+3  2 X^2+X+3  1 X^2+X+2 X^2+1  1 X+2 X^2+3  X  1 X^2+2 X^2+X+1  1 X^2+X X+2  0 X^2+3  1 X+2 X^2+3 X+3 X^2  3  1 X^2+1 X^2+X+3 X^2+X+2 X^2+X X+1 X^2+X+3 X^2+1 X+3  1  2  0 X^2 X^2+X+1 X^2+1  3 X^2+X  0 X+3  0 X^2+X X+2  1 X+1 X^2+X+3  1 X^2+1 X^2 X^2+X  1
 0  0  0  2  2  0  2  2  2  0  0  2  0  2  0  2  0  2  0  0  2  2  0  2  0  0  0  2  2  2  0  0  0  0  2  0  0  2  2  0  0  2  0  2  2  2  2  0  2  0  2  0  0  0  0  2  2  0

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+586x^54+712x^55+1372x^56+1160x^57+1372x^58+800x^59+853x^60+424x^61+410x^62+208x^63+194x^64+16x^65+64x^66+8x^67+11x^68+1x^72

The gray image is a code over GF(2) with n=464, k=13 and d=216.
This code was found by Heurico 1.16 in 1.92 seconds.