The generator matrix

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

generates a code of length 65 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+183x^56+518x^57+970x^58+1488x^59+1636x^60+2158x^61+2046x^62+2964x^63+2792x^64+3238x^65+2770x^66+3090x^67+2511x^68+2096x^69+1404x^70+1116x^71+718x^72+544x^73+216x^74+170x^75+89x^76+22x^77+18x^78+4x^79+2x^80+4x^84

The gray image is a code over GF(2) with n=260, k=15 and d=112.
This code was found by Heurico 1.13 in 15.8 seconds.