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

generates a code of length 86 over Z2[X]/(X^4) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+61x^80+62x^82+64x^83+129x^84+128x^85+1106x^86+320x^87+70x^88+18x^90+38x^92+30x^94+20x^96+1x^164

The gray image is a linear code over GF(2) with n=688, k=11 and d=320.
This code was found by Heurico 1.16 in 0.875 seconds.