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  X  1 X^2  1  1  1  1  1  1  1  1  X  1  X  1  1  0  1  1  X  1  1  1 X^2+2  1  2  1
 0  X  0  X  2  0 X+2  X X^2 X^2+X X^2 X^2+X X^2+2 X^2 X^2+X+2 X^2+X  0  2 X+2 X+2  0 X^2 X+2 X^2+X X^2 X^2+X+2  2 X^2+2 X^2 X^2+X  X X+2 X^2+X  X  0 X+2 X^2+X+2 X^2+X+2  0 X^2+X X^2+2 X^2 X+2 X+2 X^2+X X^2+2 X^2  X X^2+X  0  2  2 X^2+2  0  X X^2+X+2 X^2 X^2+X+2
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^2+X+2  X X^2+2  0 X^2+X X+2  2  0 X^2+X+2 X^2+X X^2+2 X^2+2 X^2+X X+2 X^2+2 X^2+2 X^2+X+2 X+2  0 X+2  0  2 X^2+X+2 X+2 X+2 X^2  0  2  X X^2+X+2 X^2+X X^2  2  2  0 X^2+X X^2+X X+2  2 X^2 X^2  X  0  X X^2+2 X+2  0  X X^2
 0  0  0  2  2  2  0  2  0  2  2  0  2  0  0  2  2  0  2  0  0  2  0  2  2  0  2  0  0  0  2  2  2  0  0  2  0  2  0  0  2  0  2  0  2  0  2  2  2  2  0  2  0  2  0  2  0  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+159x^54+16x^55+406x^56+256x^57+535x^58+208x^59+254x^60+32x^61+101x^62+57x^64+5x^66+17x^68+1x^100

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 0.218 seconds.