The generator matrix

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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+148x^69+414x^70+784x^71+1107x^72+1416x^73+1616x^74+2036x^75+2325x^76+2522x^77+2661x^78+2706x^79+2890x^80+2528x^81+2458x^82+2054x^83+1462x^84+1184x^85+925x^86+658x^87+367x^88+240x^89+100x^90+78x^91+37x^92+18x^93+15x^94+4x^95+3x^96+8x^97+2x^98+1x^102

The gray image is a linear code over GF(2) with n=316, k=15 and d=138.
This code was found by Heurico 1.16 in 52.8 seconds.