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 X^2  1  1  1  1 X^2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  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^3+X^2  0  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^2 X^2 X^3 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^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2 X^3  0 X^3+X^2 X^2 X^3+X^2 X^2 X^3  0 X^3 X^2  0 X^3+X^2  0 X^3 X^3+X^2 X^2 X^3  0 X^3 X^3+X^2 X^2 X^3  0  0 X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^2  0 X^3+X^2 X^3 X^2 X^2 X^3 X^3 X^3 X^3+X^2 X^2 X^2
 0  0 X^3  0  0  0  0  0  0  0  0 X^3  0 X^3 X^3  0  0  0  0  0  0  0  0  0 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3  0 X^3  0  0
 0  0  0 X^3  0  0  0 X^3  0  0  0  0 X^3  0  0 X^3  0  0  0  0  0  0  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 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  0  0  0 X^3 X^3  0  0  0  0 X^3  0 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  0  0 X^3  0  0  0 X^3  0  0  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3 X^3 X^3  0
 0  0  0  0  0 X^3  0 X^3  0  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0  0  0 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0  0  0 X^3  0  0 X^3  0 X^3  0
 0  0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  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  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  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+97x^80+148x^82+253x^84+1152x^85+124x^86+128x^87+62x^88+12x^90+34x^92+36x^94+1x^164

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 5.78 seconds.