The generator matrix

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

generates a code of length 65 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+90x^56+208x^57+490x^58+640x^59+927x^60+1064x^61+1161x^62+1404x^63+1417x^64+1600x^65+1507x^66+1500x^67+1220x^68+996x^69+817x^70+476x^71+354x^72+204x^73+129x^74+68x^75+49x^76+20x^77+22x^78+8x^79+6x^80+4x^81+2x^82

The gray image is a code over GF(2) with n=260, k=14 and d=112.
This code was found by Heurico 1.16 in 12.6 seconds.