The generator matrix

 1  0  0  0  0  1  1  1  2  1  1  0  1 X+2  2  1  1  X  2  1  1 X+2  1  2  1  2  X  1  1  1  1  2  1  X  1  1  1  1  0  1  1  1  X  1  1  1  1  X X+2 X+2  0  1  1  1  X X+2  X  X  2  2  2  2  1  1  1
 0  1  0  0  0  0  0  0  0  1  1  1 X+1  1  1 X+1  2  2  2  2  3  1  3  1 X+2  X  1  0 X+3  X  3  1 X+3  2 X+2  3 X+2 X+1  1  0 X+2  2  1 X+3  1  1 X+2  X X+2  0 X+2 X+1  X  1  1  1  1  1  1  X  1  1  3 X+2  2
 0  0  1  0  0  0  1  1  1  3  1  2  X X+3 X+1  0 X+1 X+2  1  2 X+3 X+3  2  X  2  1  3  3 X+1  1  X  0 X+2  0 X+2 X+2  X X+1  2  1  2  3 X+1  0 X+3 X+3  1  0  1  1  1  X  2 X+1  1 X+2  0 X+2  X  1  3  0 X+1  3  0
 0  0  0  1  0  1  1  0  3  2 X+1 X+3  0  1  X  3  1  1  3 X+1  0 X+2  2  3 X+2 X+2  3  0  1  3  3  X  1  1 X+1 X+1 X+2 X+3  1 X+1  0 X+3 X+1  2  X  2  0  0  2 X+1  X X+1 X+1 X+2 X+1  1  1 X+2  X  3  2 X+3  3 X+1  2
 0  0  0  0  1  1  2  3  1  0 X+1 X+3  1  X X+3 X+2 X+3  3  X  X X+1  2 X+2  0 X+1 X+3  3  X  X  0 X+3  1  X X+3  0  3  X X+2  0 X+3 X+1 X+2  X  1  1  2  0  1  1  X  0  0  3 X+3  3 X+3  1  X  1 X+2 X+3  1  3 X+3 X+2
 0  0  0  0  0  2  0  2  2  0  2  2  2  0  2  0  2  2  0  0  2  0  0  0  2  2  2  0  0  0  0  0  2  0  2  0  2  2  2  0  0  2  2  0  0  2  2  2  0  2  0  2  0  2  0  0  2  2  2  2  0  2  2  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+202x^55+571x^56+1110x^57+1785x^58+2418x^59+3208x^60+4092x^61+4747x^62+5322x^63+5844x^64+6228x^65+6239x^66+5880x^67+5065x^68+3996x^69+3219x^70+2230x^71+1478x^72+946x^73+436x^74+242x^75+139x^76+72x^77+22x^78+22x^79+14x^80+4x^81+4x^83

The gray image is a code over GF(2) with n=260, k=16 and d=110.
This code was found by Heurico 1.13 in 60.3 seconds.