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

generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+28x^74+48x^75+91x^76+142x^77+167x^78+162x^79+168x^80+204x^81+195x^82+188x^83+132x^84+118x^85+121x^86+68x^87+43x^88+50x^89+21x^90+20x^91+35x^92+12x^93+9x^94+4x^95+10x^96+2x^97+2x^98+4x^99+2x^103+1x^134

The gray image is a linear code over GF(2) with n=328, k=11 and d=148.
This code was found by Heurico 1.16 in 0.654 seconds.