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

generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+129x^68+504x^69+633x^70+1170x^71+1240x^72+1894x^73+1800x^74+2522x^75+2229x^76+3070x^77+2395x^78+3274x^79+2275x^80+2634x^81+1642x^82+1802x^83+1203x^84+970x^85+490x^86+404x^87+205x^88+136x^89+71x^90+36x^91+10x^92+8x^93+6x^94+8x^95+3x^96+3x^98+1x^100

The gray image is a linear code over GF(2) with n=312, k=15 and d=136.
This code was found by Heurico 1.16 in 52 seconds.