The generator matrix

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

generates a code of length 74 over Z2[X]/(X^4) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+128x^67+650x^68+1436x^69+2018x^70+2904x^71+3511x^72+3766x^73+4251x^74+4056x^75+3436x^76+2570x^77+1747x^78+1100x^79+559x^80+326x^81+156x^82+56x^83+34x^84+26x^85+18x^86+12x^87+1x^88+4x^89+1x^90+1x^94

The gray image is a linear code over GF(2) with n=592, k=15 and d=268.
This code was found by Heurico 1.16 in 14.3 seconds.