The generator matrix

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

generates a code of length 65 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+366x^59+1153x^60+2064x^61+3002x^62+3762x^63+4509x^64+4004x^65+4045x^66+3546x^67+2816x^68+1566x^69+1009x^70+518x^71+167x^72+132x^73+47x^74+28x^75+17x^76+10x^77+1x^78+4x^79+1x^80

The gray image is a code over GF(2) with n=520, k=15 and d=236.
This code was found by Heurico 1.16 in 9.92 seconds.