The generator matrix

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

generates a code of length 65 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+111x^60+250x^61+251x^62+228x^63+251x^64+220x^65+127x^66+130x^67+109x^68+78x^69+94x^70+66x^71+39x^72+24x^73+25x^74+22x^75+8x^76+4x^77+5x^78+2x^79+1x^80+2x^82

The gray image is a code over GF(2) with n=260, k=11 and d=120.
This code was found by Heurico 1.11 in 0.187 seconds.