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

generates a code of length 86 over Z2[X]/(X^4) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+170x^82+64x^83+262x^84+396x^85+360x^86+388x^87+178x^88+28x^89+126x^90+12x^91+38x^92+8x^93+16x^94+1x^160

The gray image is a linear code over GF(2) with n=688, k=11 and d=328.
This code was found by Heurico 1.16 in 0.813 seconds.