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 X^2  1  1  1  1  1 X^2  1  1  1  1  1  X  1  1  1  1 X^2  X  1  1 X^2  1 X^2  X  1  0 X^2  1  0  1  1  0 X^2
 0  X  0  0  0 X^2  0 X^2  0  X  X X^2+X  X X^2+X X^2+X  X X^2  X X^2  0  0  X  X X^2+X  0  X  X X^2  0 X^2+X X^2+X X^2  X  0 X^2+X  0  0 X^2+X  X X^2  X  X  0  X X^2 X^2+X  X X^2 X^2  0  0 X^2+X  0 X^2+X X^2 X^2 X^2+X X^2  0  X X^2+X  0 X^2  X  X X^2  X  0 X^2  X  0 X^2+X  X X^2+X X^2  X X^2 X^2  X  X  X  X  0
 0  0  X  0  0 X^2  X  X  X X^2+X  X X^2  X X^2+X  0  0  0  X X^2+X X^2+X X^2  0 X^2+X X^2 X^2+X X^2+X  0 X^2 X^2+X  0 X^2+X  0 X^2+X X^2 X^2+X X^2+X  0  0 X^2 X^2+X X^2+X X^2  X  X  0  0  X X^2+X X^2  X  X  0  X X^2+X  0  0 X^2 X^2  X  X X^2+X  X  0  0  X X^2+X X^2+X X^2  X  X  X  0 X^2+X X^2 X^2 X^2  0  0 X^2+X X^2+X  0 X^2 X^2
 0  0  0  X  0  X  X X^2+X X^2  0  X  X  0 X^2+X  X X^2 X^2+X X^2+X  0  0 X^2 X^2+X X^2  X  X X^2+X  0  0  X  0 X^2 X^2+X X^2  X X^2+X X^2+X X^2  0  0  X  X  X X^2 X^2  X X^2+X  0  X X^2 X^2+X X^2  0  X X^2+X  0  X X^2+X  X  0 X^2  0  0 X^2 X^2  X X^2+X  X X^2 X^2  0 X^2+X  0 X^2+X X^2+X X^2 X^2+X  X X^2  X X^2  X  X X^2
 0  0  0  0  X  X X^2  X X^2+X  X  X  0  0 X^2  X  X  0  X X^2+X  0 X^2+X X^2  0 X^2+X X^2  0 X^2  0 X^2+X  X X^2+X X^2+X X^2 X^2+X X^2+X  X X^2+X  0 X^2+X X^2 X^2  X  X X^2 X^2  0 X^2+X X^2+X  0  0 X^2 X^2  X  0  0  X X^2 X^2+X  X X^2+X  0 X^2+X  0 X^2+X  0  X  X X^2+X  0 X^2 X^2+X X^2+X  X X^2+X X^2 X^2  0 X^2+X X^2  X  0  X  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+203x^76+20x^77+76x^78+108x^79+189x^80+244x^81+66x^82+300x^83+156x^84+220x^85+50x^86+100x^87+118x^88+28x^89+42x^90+4x^91+72x^92+18x^94+28x^96+4x^98+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 3.79 seconds.