The generator matrix

 1  0  1  1  1 X+2  1  1  2  X  1  1  1  X  1 X+2  1  1  1  1  2  2  1  1  1  0  2  1  1  1  1 X+2 X+2  1  1  0  1  2  1  1  1  1  1  1 X+2  1  1 X+2  X  1  1  1  1  X  1 X+2  1  0  1  1  1  X  1  2  1
 0  1  1  0 X+3  1  X X+1  1  1 X+2  3 X+1  1 X+2  1  2  3  X X+1  1  1  0  X  3  1  1 X+3  3  1  2  1  1  1 X+3  1  1  1  X X+3  X X+3  2  X  1  0 X+2  1  1  X  1 X+1  0  1  3  1  2  1  X  0 X+2  2 X+1  1  0
 0  0  X  0 X+2  0  0  0  2  2  0  2  X X+2  X X+2  X X+2  X  2 X+2  X X+2  X  0  2  X  0 X+2  0  2  0  X  0 X+2  X X+2  X X+2 X+2  0  X  X  2  2  2  0  2  2  0  X  X X+2  0  0 X+2  X  2  0  X X+2  X  0  X  0
 0  0  0  X  0  0  X  2 X+2  X  0  0  X  0 X+2 X+2  2  X  0 X+2  2 X+2  X  0 X+2  X  2  X  X  0  X  X  X X+2  2 X+2  2  2 X+2 X+2 X+2  2 X+2  2  2  2  2 X+2  0  X  X  0  0  0  0  0  X  X  2  0  2  0 X+2  2  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  2  2  2  2  2  2  0  0  0  2  2  2  0  2  0  2  0  0  2  0  2  2  2  2  0  2  0  0  0  0  2  0  0  0  2  0  2
 0  0  0  0  0  2  0  2  2  2  2  0  0  0  2  2  0  2  2  2  0  0  0  0  0  2  2  2  0  0  2  2  2  2  2  0  0  0  0  0  2  2  0  0  2  2  2  0  0  0  2  0  2  0  2  2  2  2  2  0  0  2  0  2  0
 0  0  0  0  0  0  2  0  2  0  2  2  0  0  2  2  0  0  2  0  2  2  2  0  0  2  2  0  0  2  0  0  0  2  2  0  2  0  0  2  0  0  2  2  2  0  2  0  2  0  2  2  2  0  2  2  0  0  0  2  0  2  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+36x^56+92x^57+159x^58+396x^59+370x^60+712x^61+491x^62+928x^63+506x^64+984x^65+524x^66+858x^67+467x^68+670x^69+300x^70+330x^71+118x^72+82x^73+48x^74+34x^75+31x^76+18x^77+12x^78+14x^79+6x^80+2x^81+1x^82+1x^86+1x^88

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 4.39 seconds.