The generator matrix

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

generates a code of length 65 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+247x^58+264x^59+717x^60+468x^61+824x^62+548x^63+860x^64+600x^65+921x^66+524x^67+681x^68+376x^69+446x^70+188x^71+252x^72+88x^73+103x^74+12x^75+41x^76+4x^77+18x^78+7x^80+1x^82+1x^84

The gray image is a code over GF(2) with n=260, k=13 and d=116.
This code was found by Heurico 1.16 in 15.9 seconds.