The generator matrix

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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+64x^67+163x^68+256x^69+293x^70+390x^71+520x^72+672x^73+695x^74+868x^75+1095x^76+1162x^77+1434x^78+1400x^79+1312x^80+1192x^81+1069x^82+916x^83+710x^84+544x^85+403x^86+362x^87+222x^88+228x^89+155x^90+88x^91+54x^92+38x^93+46x^94+8x^95+17x^96+4x^97+1x^98+1x^100+1x^108

The gray image is a linear code over GF(2) with n=316, k=14 and d=134.
This code was found by Heurico 1.16 in 61.8 seconds.