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

generates a code of length 97 over Z2[X]/(X^4) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+128x^93+88x^94+64x^95+446x^96+640x^97+432x^98+64x^99+128x^101+56x^102+1x^192

The gray image is a linear code over GF(2) with n=776, k=11 and d=372.
This code was found by Heurico 1.16 in 14.2 seconds.