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

generates a code of length 85 over Z2[X]/(X^4) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+130x^80+64x^82+128x^83+356x^84+768x^85+288x^86+128x^87+92x^88+32x^90+44x^92+16x^96+1x^160

The gray image is a linear code over GF(2) with n=680, k=11 and d=320.
This code was found by Heurico 1.16 in 0.969 seconds.