The generator matrix

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

generates a code of length 91 over Z2[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+198x^81+579x^82+896x^83+1253x^84+1430x^85+2025x^86+1940x^87+2295x^88+2416x^89+2414x^90+2322x^91+2564x^92+2332x^93+2110x^94+1942x^95+1676x^96+1282x^97+1173x^98+672x^99+541x^100+296x^101+188x^102+108x^103+50x^104+28x^105+20x^106+6x^107+4x^108+2x^109+3x^110+2x^111

The gray image is a linear code over GF(2) with n=364, k=15 and d=162.
This code was found by Heurico 1.16 in 62.7 seconds.