The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+314x^58+168x^59+731x^60+328x^61+1088x^62+372x^63+1087x^64+364x^65+1067x^66+368x^67+833x^68+272x^69+519x^70+100x^71+315x^72+60x^73+127x^74+16x^75+32x^76+21x^78+9x^80

The gray image is a code over GF(2) with n=260, k=13 and d=116.
This code was found by Heurico 1.16 in 22.4 seconds.