The generator matrix

 1  0  0  0  1  1  1  1  2  1  1  1  2 X^2+2 X^2+X  1  1  1 X^2+X  0 X^2 X^2 X^2  1  1  X  1  1  1  1  1  X  1  1  X X^2+2 X+2  1  1  1  2 X^2+X+2  0  1  X  0  0 X^2+X+2  1  1  1 X+2  1  1  1 X^2  1  X  1  0
 0  1  0  0  0  2  1  3  1 X^2+2 X+3 X+1  1  1 X^2+2 X^2+X+3 X+1 X^2+1  1  1  1 X^2+X+2 X+2 X^2+X+2  1  1  0 X^2 X^2+X  1 X+2 X^2+X+2 X^2+1 X^2+X+3  1  1  1 X^2+2 X^2+2 X^2+2 X^2+2  1 X+2  3 X+2 X^2+2  2  1 X^2+X+3 X^2+1 X+1  1 X+1  X X^2+3  1 X^2+1 X^2+X+2  X X^2+X+2
 0  0  1  0 X^2  3  2  1  1 X^2+X+1 X+1  0 X^2+1  X  1 X^2+X+3  X  X X^2+X+3 X^2 X^2+X X^2  1 X+1 X+3 X+3 X+2 X^2+X+2 X^2+1  3 X^2+X+3  X X^2+X+2 X^2+1  1  0 X+1  3  X X^2+X+3  1 X+1  1 X^2 X+2  1  1 X^2+2  1  0  2 X^2+1 X+3 X^2+1 X^2+X+3 X^2+2  0  1 X^2+X+2  0
 0  0  0  1 X^2+X+1  1  3  2  1 X^2+2 X^2+X+3  0 X^2+2 X^2+X+3 X^2+X+3  3  2  1 X+3 X^2+X X^2+3  1  2 X^2+X+2 X^2+X  X X^2+3 X^2+X+2 X^2+X+1  X  0  1 X^2+2 X^2+X+1 X^2+X+1 X+1  2 X^2+2 X+1  X  2 X^2+1 X+3 X+2  1 X^2+X+2 X^2+X+1 X+1  X X^2+X+1 X^2+1 X^2+3 X^2+X+2 X^2+3 X^2+3  3 X^2+X+1 X^2+X X^2+X+2  1
 0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  2  0  0  2  0  2  2  0  2  2  0  2  0  0  2  2  0  2  0  0  2  2  0  0  0  2  2  2  2  2  0  0  0  0  0  0  0  2  2  2

generates a code of length 60 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+570x^53+1843x^54+4336x^55+6874x^56+10770x^57+14227x^58+17754x^59+18283x^60+17496x^61+15120x^62+10986x^63+6418x^64+3802x^65+1473x^66+712x^67+222x^68+108x^69+39x^70+18x^71+9x^72+4x^73+2x^74+2x^75+1x^76+2x^77

The gray image is a code over GF(2) with n=480, k=17 and d=212.
This code was found by Heurico 1.16 in 125 seconds.