The generator matrix

 1  0  0  0  1  1  1  X  1  1  2  1  X  1  2  1  0  X  2  1  1 X+2  1  0  1  X  1  2  X  1  0  1  1  1 X+2  1  1  1  1  0  1  1  1  0  1  1  2  1  1  1  X  2  0  1  2  1  1  1  1  X  1  1  X  X  1
 0  1  0  0  X  X X+2 X+2 X+1 X+3  1  1  1  3  1  X  X  1  0  1 X+1  1  1  1  2  1  0 X+2  1  2  0  1  1  0  2 X+1 X+3  1 X+2  1  0  3  2  X  0  X  1  2  2 X+3  1  1  2  1  1 X+1  2 X+2  3  0 X+3  2  X  0 X+2
 0  0  1  0  X X+3 X+3  1 X+1 X+2  3  2  X X+3 X+1 X+3  1  3  1 X+1  3  2  2 X+2  X X+2  1  X  1  X X+2  1  1 X+3  1  2 X+2  0  1  1  1  3 X+1  1  2  X X+1 X+2 X+2 X+2  0 X+3  0  X  0  0  1  3 X+2  1  3  0  0  1 X+1
 0  0  0  1 X+1 X+3  X X+3 X+3 X+2 X+1 X+3  1  X  2  0  3  X  X  1 X+2 X+1  3  0  2 X+3  1  1 X+1 X+1  1  3  0 X+1  0  X  3  2 X+2  1  1 X+1  X X+3 X+1  3  0 X+2 X+2  2 X+1  X  1 X+2  2  3 X+1  1  2 X+1 X+1  1  1  1  3
 0  0  0  0  2  2  2  2  2  2  0  0  2  0  2  0  0  0  2  0  2  2  2  2  2  0  0  0  2  0  2  0  2  2  2  2  0  0  0  2  2  2  2  2  0  2  0  0  2  2  0  0  2  2  2  2  2  2  0  0  2  0  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+208x^58+304x^59+578x^60+632x^61+801x^62+736x^63+754x^64+700x^65+648x^66+628x^67+502x^68+444x^69+491x^70+224x^71+243x^72+140x^73+84x^74+28x^75+30x^76+4x^77+6x^78+4x^80+2x^82

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 2.78 seconds.