The generator matrix

 1  0  0  0  1  1  1  1  1  1  1 X^2  X  0 X^2 X^2+X X^2 X^2+X  1  1  1  X  1  X  1 X^2+X  1  1  X  1 X^2+X  1 X^2+X  1  1 X^2 X^2 X^2  X  X X^2+X  0  1  1 X^2+X  1  0  1  X  1  1  0  X  1  1  1  1  1 X^2+X  1 X^2+X  0  1  1  1  0 X^2  1  1  1 X^2+X  1 X^2+X X^2+X  1  1  0 X^2+X  1
 0  1  0  0  0  0  1 X^2+X+1  1  1 X^2+X  1  1 X^2+X  1  1  X  1 X+1 X^2+X X^2+X+1  0 X+1  1  1  1  0  0 X^2+X X^2+X X^2+X X^2 X^2+X X^2+1 X^2+X  1  1  1  1  1  0  X  X  1  1 X^2  0  1  1 X^2+1  1  1 X^2 X^2 X^2+X X^2  0 X^2+X+1  1 X+1  1  1  0 X^2+X  0  1  1 X+1 X^2+X+1 X^2+1  0 X^2  1 X^2 X+1 X^2+X+1 X^2  1  0
 0  0  1  0  0  1  0  1 X^2+1 X^2  1 X^2+X+1 X^2+1  1 X^2+X  1  1 X+1 X^2  X X+1 X^2+X X^2 X^2  1  0 X+1  X  1 X^2+X  1  1 X^2  1 X+1  1  0  1 X^2+X+1 X^2+X  1  1 X^2+1 X^2+1 X^2  X X^2  0 X^2+X+1 X^2+X X^2+X+1 X^2+X+1  1  X X^2+X  1 X^2+X X^2+X+1  0  1  X X^2+X+1 X^2+X+1 X^2 X+1 X+1 X+1  0 X^2+1  X  0 X^2  X  1  1 X^2+X+1  1 X^2+1  0
 0  0  0  1  1 X+1 X^2+X+1 X^2+1 X^2  X X^2+X X^2+1 X^2+X X+1 X^2+X+1  1 X^2+1 X^2 X^2+X X^2+1  0  1 X^2+1  1 X^2+1 X^2  0 X^2  X  0 X^2+X+1 X^2+1  1  X X^2+X+1 X^2+1 X^2+X X^2+X X^2+X+1 X^2+X+1 X+1 X^2+X X^2  1  1  1  1 X^2  X X^2+1 X+1  1  1  X X^2  0 X^2+1  X  0 X+1 X+1  0 X^2+X+1 X^2 X^2+1 X^2  X X^2 X^2  1  1  X  1  0  0 X^2  X  1 X^2
 0  0  0  0  X  X  X  X  0  0  0 X^2+X  0 X^2+X X^2+X  X X^2+X  0 X^2 X^2+X X^2 X^2+X X^2+X  X  X  0 X^2  0 X^2 X^2  X  0  0 X^2+X  0 X^2  X X^2+X X^2  0  0  X X^2+X X^2 X^2 X^2+X  0 X^2+X  X X^2  X  0 X^2  0 X^2+X X^2+X  X X^2+X X^2+X X^2+X X^2 X^2+X  X  X X^2+X  X  X X^2  X  X X^2+X  X X^2+X X^2  0  X  X X^2+X X^2+X
 0  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2  0  0  0 X^2  0  0 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+176x^69+378x^70+764x^71+1082x^72+1444x^73+1615x^74+2014x^75+2367x^76+2572x^77+2814x^78+2634x^79+2743x^80+2516x^81+2444x^82+2004x^83+1580x^84+1216x^85+808x^86+716x^87+382x^88+216x^89+125x^90+54x^91+37x^92+44x^93+8x^94+6x^95+8x^97

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 55 seconds.