The generator matrix

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

generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+170x^73+191x^74+354x^75+162x^76+246x^77+182x^78+146x^79+88x^80+142x^81+67x^82+90x^83+19x^84+62x^85+28x^86+46x^87+9x^88+16x^89+8x^90+4x^91+8x^92+4x^93+4x^94+1x^100

The gray image is a linear code over GF(2) with n=312, k=11 and d=146.
This code was found by Heurico 1.11 in 0.281 seconds.