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

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+74x^55+122x^56+176x^57+256x^58+316x^59+377x^60+520x^61+533x^62+674x^63+735x^64+696x^65+844x^66+646x^67+568x^68+418x^69+298x^70+246x^71+182x^72+198x^73+100x^74+84x^75+54x^76+38x^77+17x^78+6x^79+8x^80+2x^81+2x^83+1x^92

The gray image is a code over GF(2) with n=260, k=13 and d=110.
This code was found by Heurico 1.16 in 5.52 seconds.