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

generates a code of length 89 over Z2[X]/(X^4) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+154x^84+32x^86+621x^88+512x^89+480x^90+184x^92+57x^96+6x^100+1x^168

The gray image is a linear code over GF(2) with n=712, k=11 and d=336.
This code was found by Heurico 1.16 in 3.45 seconds.