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  1  X  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  X  X  X  0  X  X  X  X  X  X  X  X  X  0  0  0  0  0  X  0  X  0  X  0  X  0  X  X  X  0  0  X  0
 0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  X  X  0  0  X  X  X  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  0  0  X  X  X  0  0  X  0  0
 0  0  0  X  0  0  0  X  X  X  X  X  0  X  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  X  0  0  0  0  0  0  0  X  X  0  0  0  X  X  X  X  X  0  X  0  0  0  0  0
 0  0  0  0  X  0  X  X  X  0  0  0  0  X  X  X  X  0  0  0  X  X  X  X  X  X  0  0  0  0  X  X  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  X  X  0  X  X  0  0  0  0  0  X  X  X  X  0  0  0  0  X  X  0  0  0  0  0  X  0  X  X  X  0  0  X  X  0  0
 0  0  0  0  0  X  X  0  X  X  0  X  X  X  0  0  X  0  X  X  X  0  0  X  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  0  X  X  0  X  0  X  X  0  0  0  X  X  0  0  X  X  0  0  X  X  0  0  0  0  X  X  X  0  0  X  X  X  0  0  0  0  0

generates a code of length 84 over Z2[X]/(X^2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+17x^80+10x^82+32x^83+8x^84+32x^85+15x^86+6x^88+6x^90+1x^166

The gray image is a linear code over GF(2) with n=168, k=7 and d=80.
This code was found by Heurico 1.16 in 0.113 seconds.