The generator matrix

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

generates a code of length 98 over Z2[X]/(X^3) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+96x^87+165x^88+194x^89+291x^90+156x^91+491x^92+234x^93+731x^94+230x^95+1049x^96+190x^97+951x^98+180x^99+874x^100+164x^101+682x^102+150x^103+434x^104+138x^105+207x^106+132x^107+121x^108+78x^109+53x^110+66x^111+54x^112+22x^113+23x^114+12x^115+10x^116+4x^117+6x^118+2x^119+1x^136

The gray image is a linear code over GF(2) with n=392, k=13 and d=174.
This code was found by Heurico 1.16 in 69.8 seconds.