The generator matrix

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

generates a code of length 93 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+61x^82+358x^83+494x^84+946x^85+1085x^86+1640x^87+1663x^88+2146x^89+1888x^90+2798x^91+1994x^92+2924x^93+2038x^94+2564x^95+2101x^96+2210x^97+1464x^98+1564x^99+815x^100+796x^101+455x^102+300x^103+201x^104+114x^105+42x^106+54x^107+24x^108+12x^109+6x^110+2x^113+1x^114+2x^115+1x^116+2x^117+2x^120

The gray image is a linear code over GF(2) with n=372, k=15 and d=164.
This code was found by Heurico 1.16 in 66.3 seconds.