The generator matrix

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

generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+284x^76+376x^77+1066x^78+848x^79+1810x^80+1292x^81+2479x^82+1676x^83+3100x^84+1924x^85+3145x^86+2032x^87+3171x^88+1764x^89+2545x^90+1224x^91+1575x^92+708x^93+705x^94+328x^95+350x^96+80x^97+150x^98+28x^99+61x^100+16x^102+8x^103+16x^104+6x^106

The gray image is a linear code over GF(2) with n=344, k=15 and d=152.
This code was found by Heurico 1.16 in 60.8 seconds.