The generator matrix

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

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+150x^81+325x^82+512x^83+497x^84+698x^85+470x^86+752x^87+613x^88+694x^89+538x^90+562x^91+435x^92+528x^93+299x^94+390x^95+192x^96+198x^97+140x^98+78x^99+44x^100+26x^101+15x^102+10x^103+10x^104+6x^105+3x^106+4x^109+2x^114

The gray image is a linear code over GF(2) with n=356, k=13 and d=162.
This code was found by Heurico 1.16 in 5.49 seconds.