The generator matrix

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

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+88x^56+266x^57+446x^58+634x^59+693x^60+1286x^61+1104x^62+1598x^63+1336x^64+1784x^65+1248x^66+1558x^67+1020x^68+1166x^69+741x^70+598x^71+276x^72+212x^73+150x^74+88x^75+39x^76+20x^77+18x^78+4x^79+3x^80+2x^81+4x^82+1x^86

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 12.5 seconds.