The generator matrix

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

generates a code of length 98 over Z2[X]/(X^4) who´s minimum homogenous weight is 94.

Homogenous weight enumerator: w(x)=1x^0+94x^94+316x^95+206x^96+496x^97+188x^98+176x^99+174x^100+128x^101+83x^102+132x^103+18x^104+32x^105+1x^110+2x^122+1x^136

The gray image is a linear code over GF(2) with n=784, k=11 and d=376.
This code was found by Heurico 1.16 in 1.25 seconds.