The generator matrix

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

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+76x^73+212x^74+152x^75+250x^76+134x^77+249x^78+124x^79+209x^80+94x^81+127x^82+96x^83+140x^84+38x^85+43x^86+22x^87+30x^88+22x^89+6x^90+4x^91+7x^92+4x^93+2x^94+2x^95+2x^96+1x^100+1x^114

The gray image is a linear code over GF(2) with n=316, k=11 and d=146.
This code was found by Heurico 1.16 in 0.583 seconds.