The generator matrix

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

generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+253x^74+798x^75+1294x^76+1930x^77+2791x^78+3894x^79+5348x^80+6552x^81+7659x^82+9010x^83+9611x^84+10422x^85+11233x^86+10564x^87+10350x^88+9430x^89+7583x^90+6662x^91+5286x^92+3790x^93+2570x^94+1638x^95+1057x^96+580x^97+325x^98+166x^99+137x^100+50x^101+29x^102+32x^103+4x^104+14x^105+4x^106+4x^107+1x^110

The gray image is a linear code over GF(2) with n=344, k=17 and d=148.
This code was found by Heurico 1.13 in 287 seconds.