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  X  X  X  X  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^2 X^2  X  X
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^2 X^3  0 X^3+X^2 X^2 X^3  0 X^3+X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^2  0 X^3+X^2 X^3 X^2 X^3 X^2  0 X^3+X^2 X^3 X^2  0 X^3 X^2  0 X^3 X^2  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3  0  0 X^3+X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2  0 X^2 X^3+X^2 X^3+X^2 X^3  0  0 X^3 X^3 X^2 X^2  0 X^3 X^3+X^2 X^3 X^3+X^2  0
 0  0 X^3  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3  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 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3
 0  0  0 X^3  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0
 0  0  0  0 X^3  0  0  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0
 0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3  0  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0  0  0  0  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0
 0  0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3  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 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3  0  0 X^3  0  0  0  0 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+71x^92+92x^94+226x^96+256x^97+776x^98+256x^99+225x^100+76x^102+42x^104+16x^106+5x^108+3x^112+2x^116+1x^180

The gray image is a linear code over GF(2) with n=784, k=11 and d=368.
This code was found by Heurico 1.16 in 1.36 seconds.