The generator matrix

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

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+72x^76+110x^77+161x^78+84x^79+191x^80+150x^81+224x^82+84x^83+236x^84+154x^85+186x^86+76x^87+125x^88+98x^89+58x^90+12x^91+12x^92+3x^94+2x^96+4x^98+2x^102+1x^106+1x^120+1x^122

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 0.595 seconds.