The generator matrix

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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+179x^74+196x^75+286x^76+212x^77+279x^78+120x^79+204x^80+100x^81+136x^82+38x^83+73x^84+42x^85+52x^86+28x^87+23x^88+12x^89+25x^90+14x^91+21x^92+2x^93+1x^94+4x^95

The gray image is a linear code over GF(2) with n=316, k=11 and d=148.
This code was found by Heurico 1.16 in 0.461 seconds.