The generator matrix

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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+120x^71+230x^72+480x^73+471x^74+682x^75+602x^76+790x^77+574x^78+722x^79+571x^80+656x^81+485x^82+538x^83+314x^84+314x^85+196x^86+196x^87+87x^88+68x^89+26x^90+26x^91+14x^92+12x^93+8x^94+2x^95+5x^96+2x^99

The gray image is a linear code over GF(2) with n=316, k=13 and d=142.
This code was found by Heurico 1.16 in 4.56 seconds.