The generator matrix

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

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+230x^84+842x^85+1843x^86+2046x^87+3121x^88+3224x^89+4212x^90+3020x^91+3782x^92+2716x^93+2983x^94+1590x^95+1373x^96+856x^97+493x^98+200x^99+81x^100+38x^101+32x^102+40x^103+15x^104+16x^105+4x^106+5x^108+4x^109+1x^114

The gray image is a linear code over GF(2) with n=728, k=15 and d=336.
This code was found by Heurico 1.16 in 20.4 seconds.