The generator matrix

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

generates a code of length 65 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+83x^60+596x^61+932x^62+1156x^63+1153x^64+1176x^65+820x^66+768x^67+481x^68+460x^69+256x^70+160x^71+89x^72+12x^73+8x^74+12x^75+16x^76+12x^77+1x^80

The gray image is a code over GF(2) with n=520, k=13 and d=240.
This code was found by Heurico 1.16 in 0.703 seconds.