The generator matrix

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

generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+152x^74+108x^75+214x^76+52x^77+158x^78+44x^79+97x^80+8x^81+78x^82+20x^83+28x^84+4x^85+22x^86+20x^87+8x^88+4x^90+1x^96+2x^98+2x^100+1x^112

The gray image is a linear code over GF(2) with n=312, k=10 and d=148.
This code was found by Heurico 1.16 in 94.1 seconds.