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

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+62x^67+154x^68+242x^69+342x^70+396x^71+490x^72+616x^73+768x^74+966x^75+1022x^76+1098x^77+1317x^78+1498x^79+1361x^80+1186x^81+1082x^82+876x^83+748x^84+574x^85+424x^86+296x^87+232x^88+196x^89+140x^90+110x^91+75x^92+54x^93+21x^94+18x^95+12x^96+2x^97+2x^98+2x^99+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 26.9 seconds.