The generator matrix

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

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+28x^74+174x^75+50x^76+148x^77+62x^78+212x^79+52x^80+40x^81+26x^82+152x^83+22x^84+36x^85+9x^86+4x^87+2x^88+1x^96+2x^106+2x^107+1x^118

The gray image is a linear code over GF(2) with n=316, k=10 and d=148.
This code was found by Heurico 1.16 in 0.39 seconds.