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

generates a code of length 84 over Z2[X]/(X^4) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+37x^80+32x^81+186x^82+44x^83+463x^84+24x^85+158x^86+16x^87+42x^88+8x^89+6x^90+4x^91+2x^94+1x^148

The gray image is a linear code over GF(2) with n=672, k=10 and d=320.
This code was found by Heurico 1.16 in 0.515 seconds.