The generator matrix

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

generates a code of length 60 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+70x^58+119x^60+52x^62+4x^64+6x^66+1x^68+3x^72

The gray image is a code over GF(2) with n=480, k=8 and d=232.
This code was found by Heurico 1.16 in 0.172 seconds.