The generator matrix

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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+230x^73+300x^74+410x^75+389x^76+490x^77+333x^78+370x^79+237x^80+302x^81+220x^82+158x^83+132x^84+142x^85+98x^86+94x^87+46x^88+76x^89+24x^90+24x^91+11x^92+8x^93+1x^94

The gray image is a linear code over GF(2) with n=316, k=12 and d=146.
This code was found by Heurico 1.16 in 0.978 seconds.