The generator matrix

 1  0  1  1  1 X+2  1  1  0  1 X+2  1  1  2  1  1  X  1  1  1  2  0  1  1  1  1  0  1  1  0  X  1  1  0 X+2  1  X  1  1  1  1  1  1 X+2  X  2  1  1  0  1  1  1  1  1  X  0  1  1  1  X  1  1  0  1  1
 0  1  1  0  1  1  X X+3  1 X+2  1 X+3  1  1  0  X  1  3  3  2  1  1 X+3 X+2 X+2  1  1  1  0  1  1  3  X  1  1  0  1  2  0  3  1 X+3  X  1  1  1  0  X  1 X+2  1  3 X+2  X  1  2  0 X+1  0  2  0 X+1  1  0  0
 0  0  X  0  0  0  0  0  0  0  2  0  2  2  0  0  2  2  0  2  2  2 X+2  X X+2 X+2 X+2 X+2 X+2 X+2 X+2 X+2  X X+2 X+2 X+2 X+2 X+2  2 X+2  X  2  0  0  0  X  0  X X+2  X  0  2  2  X  X  2  2  X  0  0 X+2  X X+2 X+2  0
 0  0  0  X  0  0  X  2  X  2 X+2  X X+2  X  X  2  0  X  2  0 X+2  0  0 X+2  0  2  0 X+2  2  X X+2  X  X  2 X+2 X+2  0  0  X  X  2  X  X  0  X  2  0  2  0  2 X+2  2  0  X  0  2  X X+2  X  X  2  0  X  0  0
 0  0  0  0  X  0  0  X  X  2 X+2  2  2  2 X+2 X+2  X X+2  0  X  0  X  2  0  2  X X+2  X X+2  X  0  X  X  0  0  2  2 X+2  X  0  X X+2  X  X  X X+2  2  0  0 X+2 X+2  0 X+2  X  X  X  2  0  2  0  2  X X+2  X  0
 0  0  0  0  0  2  2  2  2  2  0  2  0  2  0  2  0  2  0  0  0  2  2  0  0  0  2  0  0  0  0  2  2  2  2  2  0  0  2  0  0  0  2  2  2  0  2  0  2  2  2  2  0  0  0  0  0  0  2  2  0  2  2  0  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+42x^56+94x^57+202x^58+430x^59+318x^60+688x^61+492x^62+932x^63+517x^64+932x^65+522x^66+900x^67+486x^68+668x^69+245x^70+284x^71+120x^72+122x^73+53x^74+38x^75+46x^76+20x^77+18x^78+8x^79+4x^80+4x^81+2x^82+2x^84+1x^86+1x^90

The gray image is a code over GF(2) with n=260, k=13 and d=112.
This code was found by Heurico 1.16 in 4.28 seconds.