The generator matrix

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

generates a code of length 72 over Z2[X]/(X^4) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+74x^65+620x^66+1286x^67+2305x^68+2972x^69+3771x^70+3662x^71+4059x^72+3690x^73+3571x^74+2486x^75+2032x^76+1036x^77+590x^78+308x^79+156x^80+72x^81+39x^82+10x^83+5x^84+12x^85+1x^86+6x^87+2x^88+2x^91

The gray image is a linear code over GF(2) with n=576, k=15 and d=260.
This code was found by Heurico 1.16 in 15.2 seconds.