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

generates a code of length 60 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+334x^56+64x^57+128x^58+448x^59+128x^60+448x^61+128x^62+64x^63+286x^64+18x^72+1x^96

The gray image is a code over GF(2) with n=480, k=11 and d=224.
This code was found by Heurico 1.16 in 132 seconds.