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

generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+208x^76+24x^77+116x^79+317x^80+224x^81+284x^83+206x^84+248x^85+108x^87+142x^88+16x^89+4x^91+109x^92+36x^96+4x^100+1x^140

The gray image is a linear code over GF(2) with n=332, k=11 and d=152.
This code was found by Heurico 1.16 in 6.97 seconds.