The generator matrix

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

generates a code of length 81 over Z2[X]/(X^4) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+68x^74+640x^75+1656x^76+2300x^77+2952x^78+3640x^79+3659x^80+3864x^81+3563x^82+3296x^83+2638x^84+1822x^85+1251x^86+692x^87+352x^88+180x^89+82x^90+52x^91+18x^92+22x^93+11x^94+4x^96+4x^97+1x^98

The gray image is a linear code over GF(2) with n=648, k=15 and d=296.
This code was found by Heurico 1.16 in 13.8 seconds.