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  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  X
 0 X^3+X^2  0 X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0 X^3 X^2 X^2 X^3 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^2  0 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^2  0 X^3 X^3+X^2 X^3+X^2 X^3 X^3+X^2  0 X^3 X^2  0 X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3  0 X^2 X^3  0 X^3 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2  0 X^2  0 X^2 X^2 X^3+X^2 X^2 X^2 X^3  0  0 X^3  0 X^3 X^3+X^2 X^3  0
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^2  0 X^3+X^2  0 X^2  0  0 X^3+X^2 X^2  0  0 X^3+X^2 X^2  0  0 X^3+X^2 X^2  0  0 X^3+X^2 X^2  0 X^3 X^2  0 X^3+X^2 X^3 X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^2  0 X^2 X^3 X^2 X^3  0 X^2  0 X^3+X^2 X^3 X^2 X^2 X^3 X^2  0 X^3 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3 X^3 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^2  0 X^2 X^3  0 X^2  0 X^3+X^2 X^3 X^2 X^3  0 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2  0 X^3  0  0 X^3+X^2 X^2 X^3 X^3 X^3 X^3 X^3+X^2 X^2 X^3+X^2
 0  0  0 X^3  0  0 X^3  0  0  0 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0  0  0 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0  0 X^3 X^3  0 X^3  0  0
 0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0  0  0 X^3  0  0 X^3  0  0  0
 0  0  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0  0  0  0  0 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  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0  0  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3  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+192x^94+126x^96+1408x^98+128x^100+192x^102+1x^192

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 7.48 seconds.