The generator matrix

 1  0  0  1  1  1  0 X^2 X^2 X^2  1  1  1  1  X X^2+X  1  1 X^2  1 X^2  1  1 X^2+X  1  X  1  1  1 X^2+X  1  1  1 X^2+X  1  1  1  1  1  1  0  X X^2+X  1  0  0  1  0  0  1  1  1  1 X^2  X X^2+X X^2 X^2+X X^2+X  0  X X^2+X  1  1  X  1  1  0 X^2 X^2+X X^2+X  0 X^2 X^2  1  1  X  X
 0  1  0  0 X^2+1 X^2+1  1  X  1  1 X^2 X^2 X^2+1 X^2+1 X^2+X  0 X^2+X X^2+X+1  1 X^2  1 X^2 X+1 X^2  X  1 X^2+1  X X^2+1  1  1 X+1 X^2+X  1 X^2+X+1  0 X^2+X+1 X+1  1 X^2+X X^2+X  1  X X+1  1  1  X  1  1  X X^2+X+1 X^2+X  0  0  1  1  X  1  1  X  0  1 X^2+X  X  1  X X^2+X X^2  1  1  1  X  1  1  X  0 X^2  1
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1  X  1  X X^2+1  1 X^2+X  1  1 X^2+X  0 X^2 X+1 X^2+X+1 X^2 X^2+X+1  1 X^2+1 X^2+X  X X+1  1  1 X^2+X+1  X X^2 X+1  1 X^2+1 X^2+X+1  0 X^2 X+1  1 X^2  1  X  X  X X^2+X  0  1 X^2+1  1 X^2  X  1 X^2+1 X^2+X  0 X^2  0  1  1 X^2+X+1 X^2+X  0 X^2+1 X^2+X  0  1  1 X^2+X  X  1 X^2+X X^2  X X^2+1  1  0
 0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  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+137x^74+128x^75+159x^76+132x^77+153x^78+24x^79+65x^80+44x^81+63x^82+32x^83+17x^84+16x^85+23x^86+4x^87+11x^88+4x^91+9x^92+1x^96+1x^100

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 0.283 seconds.