The generator matrix

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

generates a code of length 91 over Z2[X]/(X^4) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+836x^84+1940x^85+3262x^86+4310x^87+6124x^88+6158x^89+7393x^90+6618x^91+7231x^92+6150x^93+5670x^94+3662x^95+2688x^96+1618x^97+1031x^98+386x^99+245x^100+94x^101+63x^102+28x^103+11x^104+8x^105+4x^106+4x^107+1x^110

The gray image is a linear code over GF(2) with n=728, k=16 and d=336.
This code was found by Heurico 1.16 in 53.8 seconds.