The generator matrix

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

generates a code of length 65 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+830x^58+2356x^59+4686x^60+7328x^61+10466x^62+13336x^63+17080x^64+18648x^65+16892x^66+14740x^67+10490x^68+6704x^69+4226x^70+1824x^71+961x^72+296x^73+123x^74+32x^75+26x^76+16x^77+4x^78+4x^80+1x^82+2x^86

The gray image is a code over GF(2) with n=520, k=17 and d=232.
This code was found by Heurico 1.16 in 634 seconds.