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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+211x^80+44x^82+503x^84+308x^86+475x^88+148x^90+194x^92+12x^94+106x^96+39x^100+6x^104+1x^152

The gray image is a linear code over GF(2) with n=348, k=11 and d=160.
This code was found by Heurico 1.16 in 6.34 seconds.