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

generates a code of length 98 over Z2[X]/(X^4) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+46x^93+79x^94+78x^95+78x^96+144x^97+1251x^98+148x^99+62x^100+48x^101+35x^102+24x^103+16x^104+16x^105+8x^106+4x^107+2x^108+2x^109+2x^110+2x^111+1x^112+1x^186

The gray image is a linear code over GF(2) with n=784, k=11 and d=372.
This code was found by Heurico 1.16 in 115 seconds.