The generator matrix

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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+59x^72+66x^73+201x^74+132x^75+218x^76+140x^77+155x^78+116x^79+222x^80+132x^81+202x^82+112x^83+126x^84+44x^85+68x^86+20x^87+11x^88+2x^89+10x^90+4x^91+1x^94+1x^96+1x^98+2x^104+1x^106+1x^114

The gray image is a linear code over GF(2) with n=316, k=11 and d=144.
This code was found by Heurico 1.16 in 0.524 seconds.