The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+114x^58+5x^60+4x^62+1x^64+2x^66+1x^68

The gray image is a code over GF(2) with n=464, k=7 and d=232.
This code was found by Heurico 1.16 in 0.093 seconds.