The generator matrix

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

generates a code of length 65 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+54x^55+149x^56+216x^57+429x^58+408x^59+965x^60+838x^61+1593x^62+1094x^63+2027x^64+1006x^65+2012x^66+1050x^67+1558x^68+822x^69+926x^70+392x^71+361x^72+158x^73+147x^74+50x^75+53x^76+28x^77+9x^78+20x^79+6x^80+4x^81+2x^82+4x^83+2x^90

The gray image is a code over GF(2) with n=260, k=14 and d=110.
This code was found by Heurico 1.16 in 14.8 seconds.