The generator matrix

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

generates a code of length 98 over Z2[X]/(X^3) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+246x^89+476x^90+688x^91+888x^92+994x^93+1120x^94+1166x^95+1148x^96+1216x^97+1286x^98+1098x^99+1125x^100+972x^101+821x^102+852x^103+582x^104+406x^105+432x^106+366x^107+188x^108+108x^109+76x^110+50x^111+33x^112+24x^113+10x^114+4x^115+3x^116+2x^117+3x^118

The gray image is a linear code over GF(2) with n=392, k=14 and d=178.
This code was found by Heurico 1.13 in 7.05 seconds.