The generator matrix

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

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+32x^74+136x^75+112x^76+178x^77+78x^78+122x^79+57x^80+80x^81+38x^82+60x^83+27x^84+38x^85+30x^86+10x^87+2x^88+4x^89+2x^90+8x^91+4x^93+1x^94+2x^98+1x^100+1x^102

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 0.307 seconds.