The generator matrix

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

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+108x^58+250x^59+337x^60+220x^61+83x^62+10x^63+14x^64+1x^114

The gray image is a code over GF(2) with n=480, k=10 and d=232.
This code was found by Heurico 1.16 in 14.5 seconds.