The generator matrix

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

generates a code of length 98 over Z2[X]/(X^4) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+280x^92+374x^94+144x^95+577x^96+368x^97+732x^98+368x^99+555x^100+144x^101+254x^102+164x^104+72x^106+45x^108+8x^110+9x^112+1x^168

The gray image is a linear code over GF(2) with n=784, k=12 and d=368.
This code was found by Heurico 1.16 in 133 seconds.