The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  0 X+2  1  1  1  1 X^2 X^2+X+2  1  1  X  1  1  X  1  1 X^2  2  X  1  1  1  1  1  1  1  1  0 X^2+X+2  2  1  1  1 X^2  1  X  1  1  1 X^2+X X+2  1  1  1  0  1  1
 0  1  1 X^2+X  1 X^2+X+1 X^2  3  1 X+1 X^2+X+2  1  1  0 X^2+3  2  3  1  1 X^2+3 X^2+X+1  1 X^2+2  X  1  X X+1  1  1  1 X^2+X+3 X^2+1  0 X^2+2 X+3 X^2+2 X+2 X^2+X+2  1  1  1 X^2+X+1 X^2+X  3  1  0  1 X^2+X+1  1 X^2+X+3  1  1 X^2 X^2+3 X+3  X  0 X^2+X
 0  0  X  0 X+2  X X+2  2  0  2 X+2 X^2+X+2 X^2 X^2+2 X^2+2 X^2+X+2 X^2+X+2 X^2+X X^2+2  X X^2+2  X  0 X^2+X+2  0 X^2+2 X^2+X+2  X X^2+2 X^2+X+2  2  0 X+2 X^2+X X^2+X X^2 X^2+X+2 X^2+2 X^2+X+2  X  2 X^2+2  2 X^2 X^2+2 X^2+X+2  X X+2 X^2+X+2 X^2+X+2 X^2+X  0  0 X^2+X  2 X+2  0 X^2+X+2
 0  0  0  2  0  2  2  2  2  0  0  2  2  0  2  2  0  0  0  2  0  2  2  0  0  2  2  2  2  0  2  0  2  2  0  2  2  0  0  2  2  2  0  0  0  0  0  0  2  2  2  2  0  2  2  2  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+251x^54+508x^55+559x^56+544x^57+519x^58+552x^59+467x^60+368x^61+193x^62+60x^63+26x^64+16x^65+17x^66+8x^68+4x^70+3x^76

The gray image is a code over GF(2) with n=464, k=12 and d=216.
This code was found by Heurico 1.16 in 0.328 seconds.