The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  2  2  X  1  X  1  1  1  0  X  1  2  X  1  1  X  1  1  1  1  1  2  1  X  1  X  1  1  1  0  X  1  2  1
 0  X  0  0  0  X X+2  X  0  2  2  0  X X+2  X X+2 X+2 X+2 X+2  2  0  0 X+2 X+2  0  0  X X+2  2  0 X+2  2  X  2  2  X X+2 X+2 X+2  X X+2  2  X  0  X X+2  X  X X+2  0  X  2  0  X X+2  2  X  X  2  0  X  2  X  0  2
 0  0  X  0  X  X X+2  0  0  0 X+2 X+2  X  X  2  0  X  2  0 X+2 X+2  2 X+2 X+2 X+2  2  X  X X+2  2 X+2  X X+2  X  2  X  2  2 X+2  X  2 X+2 X+2  0  0  0  0  X  0  2  2  2  X X+2  0  0  0  X  X  0  0 X+2 X+2  X  0
 0  0  0  X  X  0 X+2  X  2 X+2  X  2  2  X  X  2  0 X+2  0  X  2  X  X X+2  2  2  0  2  X  X X+2  X  2  0  2  0  2 X+2  2 X+2  2  2  0 X+2  X X+2  X X+2  0  X X+2 X+2  X  X  0  0  2  X  0  0  2  X  0  X  X
 0  0  0  0  2  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  2  2  0  2  2  0  0  0  0  2  2  0  2  0  2  0  0  2  0  0  2  2  2  2  2  2  0  0  2  0  0  2  2  0  0  0  0  0  2  2  2  0  0  0
 0  0  0  0  0  2  0  2  0  0  2  2  0  2  2  0  0  0  2  2  2  0  0  2  2  2  0  2  0  2  2  0  0  0  2  2  2  0  0  2  0  0  0  2  2  0  0  0  0  0  2  0  2  0  2  0  2  2  2  0  2  0  2  2  0
 0  0  0  0  0  0  2  2  2  2  0  0  2  0  0  0  0  0  2  0  2  0  2  2  2  0  0  2  2  0  2  2  0  0  0  0  2  0  2  2  0  0  2  0  0  2  0  0  2  2  2  2  2  0  2  0  2  2  0  2  0  2  0  2  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+51x^56+80x^57+109x^58+118x^59+322x^60+154x^61+458x^62+116x^63+626x^64+142x^65+671x^66+114x^67+403x^68+108x^69+217x^70+74x^71+93x^72+72x^73+62x^74+24x^75+39x^76+18x^77+17x^78+2x^79+2x^81+1x^82+1x^88+1x^98

The gray image is a code over GF(2) with n=260, k=12 and d=112.
This code was found by Heurico 1.16 in 1.33 seconds.