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  X  X  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
 0 2X+2  0  0  0  2 2X+2  2  0  0  0  0  2 2X+2  2 2X+2  0  0  2 2X+2  0  2  0 2X 2X 2X+2  2  0 2X+2  0 2X  2 2X 2X+2  0 2X  2 2X  2 2X 2X+2 2X+2 2X+2 2X  2 2X 2X  2 2X  2 2X 2X+2 2X  2 2X+2 2X 2X  2 2X 2X+2
 0  0 2X+2  0  2  2 2X+2  0  0  0  2 2X+2  2 2X+2  0  0 2X 2X 2X+2  2 2X+2 2X  2  0  2 2X 2X+2  2 2X 2X 2X 2X  2 2X+2 2X 2X+2  0  0 2X+2  2  0 2X 2X+2 2X+2  2 2X  0 2X  2  2  0  2 2X+2 2X+2  0  2 2X  0 2X+2 2X
 0  0  0 2X+2  2  0 2X+2  2 2X  2 2X+2 2X 2X  2 2X+2 2X 2X  2 2X  2 2X+2 2X+2 2X  2  0  2  0  0 2X 2X+2 2X+2  2  0  0  0  2 2X 2X+2 2X+2 2X  2  0 2X 2X+2 2X+2 2X  0  0  2  2  2 2X  0  2 2X+2 2X+2  0  0 2X 2X+2

generates a code of length 60 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+24x^57+60x^58+104x^59+653x^60+104x^61+44x^62+24x^63+9x^64+1x^116

The gray image is a code over GF(2) with n=480, k=10 and d=228.
This code was found by Heurico 1.16 in 19.4 seconds.