The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  0  0  2  2  0  X  1  1  X  0  X  1  X  1  1  X  1  1
 0  X  0  0  0  0  0  0  0  0  2  X  X X+2  0 X+2 X+2  0  X  2 X+2  2  X  X  X  2  X  0  X  2 X+2  X X+2 X+2 X+2 X+2  X  2  0 X+2 X+2  2  X X+2  X  X  X  0  X  X  X  0 X+2  X  X  2  0  0  X X+2  2 X+2 X+2  0  X
 0  0  X  0  0  0  0  0  0  0 X+2  2  X  X  X  X  0  X  0  X X+2  2  0 X+2  X  X X+2 X+2  2  0 X+2  0  2 X+2  X  0  2  2  X  0  2  X X+2 X+2  X  2  2  2 X+2  2  2  2  2  2 X+2  2  0  X  2 X+2 X+2 X+2  X  0  X
 0  0  0  X  0  0  0  X X+2  X  X X+2  0  X  2  0 X+2 X+2 X+2  2 X+2  X  0  2  0  2  X  X  X  2  X  0 X+2  0  X X+2  0  2  X  X  2 X+2  0  2  X  X  0  X  2  0 X+2  0 X+2 X+2 X+2 X+2  X  2  X  2  X  0  0  0  X
 0  0  0  0  X  0  X  X  X  2  X  X  X  2  2 X+2 X+2  2  2 X+2 X+2  X X+2  2  2  X  0 X+2  2 X+2 X+2  X X+2  X  0 X+2 X+2  0  0  2  X  2  0 X+2  2  2  2  2  0  2 X+2  X  X  0 X+2  2  X X+2  X  0  2  2  2 X+2  0
 0  0  0  0  0  X  X  2 X+2 X+2  X  X X+2  0  X  2  2  2 X+2  X  0  2  2  0  X  0  X  2  2 X+2 X+2 X+2 X+2  0  2  2  2  2  0  0 X+2 X+2 X+2 X+2  X  0  0  2  X  X  X  0  2 X+2  0  0 X+2 X+2 X+2 X+2  0 X+2  X  0 X+2
 0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  0  0  0  2  2  0  0  0  0  2  2  0  2  2  0  0  0  0  2  2  2  2  2  2  0  2  0  0  0  2  2  0  0  0  0  0  0  0  0  2  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 54.

Homogenous weight enumerator: w(x)=1x^0+156x^54+516x^56+720x^58+104x^59+1039x^60+380x^61+1634x^62+888x^63+2077x^64+1324x^65+2250x^66+952x^67+1536x^68+340x^69+1012x^70+104x^71+673x^72+4x^73+348x^74+217x^76+86x^78+20x^80+2x^82+1x^104

The gray image is a code over GF(2) with n=260, k=14 and d=108.
This code was found by Heurico 1.16 in 20.4 seconds.