The generator matrix

 1  0  0  1  1  1  0  X  1  1  1  1  0  0 X^2  X  X  1  1  1 X^2  1  X X^2+X  1  1 X^2+X  1 X^2+X X^2  1  1  1  1 X^2+X  1  0  1  1 X^2+X X^2+X  1  X  1  1 X^2  1  1  1 X^2  1  1  1  1  1 X^2  X  1  1  1  1  1  1  0  1  1  1  1  1  0  X  1  1  X  1  X  0 X^2
 0  1  0  0  1  1  1 X^2 X^2 X^2 X^2+1 X^2+1  1  1  X X^2+X  1  X  1  1  1 X^2+X  1  1 X^2+1  X  0 X^2+1  1  X X^2+X X^2+1 X^2  X  1 X^2+1 X^2 X^2+X X+1 X^2+X  1  0  1 X+1 X+1  1  0 X^2+X+1  X  1 X+1 X^2+X+1 X+1 X^2+X+1 X^2+X  1  X  1 X+1 X+1  X X+1 X^2+X+1  1  1 X^2+1 X^2+X+1 X^2+X X^2+X+1  1 X^2+X  0 X^2+1  1 X^2+X  0 X^2  0
 0  0  1  1 X^2 X^2+1  1  1  X X+1 X^2+X X^2+X+1  X X^2+X+1  1  1  1  X X^2+X+1  X X^2 X^2 X+1 X^2  1 X+1  1  0  X  1 X^2+1 X^2 X^2 X^2+X X^2+X  X  1  0  0  1  0 X^2+1 X^2+X+1 X^2+X+1  X X^2+X X^2+X  1 X^2+1 X^2+X+1 X+1  1 X^2+X  0 X^2+X+1 X^2+1 X^2 X^2+X X^2 X^2+X  1  0 X^2+X X^2+X+1 X^2+X  0  X X^2+1  0 X+1 X^2 X^2  1  0 X^2+X  1  1  1
 0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  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+96x^74+188x^75+145x^76+148x^77+110x^78+70x^79+75x^80+20x^81+37x^82+40x^83+12x^84+36x^85+7x^86+4x^87+21x^88+4x^90+1x^92+4x^93+1x^94+2x^95+1x^96+1x^98

The gray image is a linear code over GF(2) with n=312, k=10 and d=148.
This code was found by Heurico 1.11 in 0.218 seconds.