The generator matrix

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

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+312x^58+188x^59+795x^60+276x^61+974x^62+400x^63+1138x^64+400x^65+1034x^66+308x^67+846x^68+300x^69+568x^70+120x^71+314x^72+40x^73+100x^74+8x^75+31x^76+8x^77+18x^78+11x^80+2x^82

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 28.5 seconds.