The generator matrix

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

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+212x^54+556x^55+1305x^56+2110x^57+3163x^58+4732x^59+6116x^60+7590x^61+9522x^62+11068x^63+11940x^64+13022x^65+12855x^66+11558x^67+9938x^68+7998x^69+6293x^70+4528x^71+2807x^72+1620x^73+940x^74+540x^75+350x^76+164x^77+69x^78+40x^79+23x^80+8x^81+2x^82+2x^83

The gray image is a code over GF(2) with n=260, k=17 and d=108.
This code was found by Heurico 1.13 in 220 seconds.