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

generates a code of length 86 over Z2[X]/(X^4) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+149x^84+220x^86+130x^88+2x^90+6x^92+1x^96+1x^100+2x^114

The gray image is a linear code over GF(2) with n=688, k=9 and d=336.
This code was found by Heurico 1.16 in 3.19 seconds.