The generator matrix

 1  0  0  0  1  1  1  1 X^3+X^2 X^3+X  1 X^2+X  X  1  1 X^3+X^2+X X^3  X  1  1  0 X^2+X  1 X^2  1  1  1  1  X  1  1 X^2  X X^2  1  1  1  1 X^3+X^2+X X^3  1 X^2+X  X  1  1  1 X^3+X^2+X  1 X^2+X X^2  1  1  1  1  1  0 X^2  1 X^3+X^2+X  X  1 X^3+X^2+X X^2  1  1 X^2+X  1 X^2  1  1 X^3+X^2+X  1  1  1  1  1 X^3+X^2+X  X X^3 X^3+X^2+X X^3+X^2+X X^3+X^2 X^3+X  1 X^3+X^2  1  1 X^3+X  1 X^2+X X^3+X  1
 0  1  0  0  X X^2+1 X^2 X^3+1  1  1 X^3+X^2+X  1 X^3+X X^2+1 X^3+X^2+1 X^3+X^2+X  1  1  X  1 X^2+X  1 X^3+X^2  1 X^3 X^3+1 X^2+1 X^3+X^2+X+1 X^3+X^2+X X^3+X^2+X X^3  1  1  X  0 X^3+X^2+X+1  X X+1 X^3 X^3+X X^2+1  1  1 X^2+1 X^2+X+1 X^3  1 X+1  1 X^3+X^2 X^3 X^2+X X^2+X X^3+1  X X^3+X^2+X  1 X^2+X+1  1  1 X^2 X^3+X^2  1 X^3+X^2+1 X^3+X^2+X  X X^3+X^2+X+1 X^2+X X^3 X^2+1 X^3+X X^3+X^2+1  0 X^2 X^3+1 X^3+X^2+X+1  1 X^3+X X^3 X^3+X^2  1  1 X^3+X^2 X^3+X^2  0 X^2 X+1 X^3+X^2+X X^3+X^2+1  1  1  0
 0  0  1  0  0 X^2  1 X^3+1 X^2+1 X^3 X^2+X+1 X^2+X+1  1 X^2+X X^3+X^2+X+1  1 X^3+X^2 X^2+X+1 X^2+X X^3+X^2+X  0 X^2 X^3+X^2 X^2+1 X^2+X+1 X^2+1 X+1 X^3+X  1 X^3+X+1 X^3+X^2+1 X^3+X^2+X X^3+X^2+1  1 X^3+1 X^3  0 X^3+X+1  1 X^2 X^3+X^2+1  0 X^2+1 X^2+X+1  X X^3+X+1 X^3+X X^2 X^3+X  1 X+1  X X^2+1  X X^3  1 X^3+X+1 X^3+X+1 X^3+X^2 X^3+X^2+X+1 X^2+X  1 X^3+X X^2+1 X^2  0 X^2  1 X^3+X^2+X X^3+X^2  1  X X^3 X^2+X X^2+X+1 X^3+X  0  1  1  1 X^2+X+1 X^3+X+1  1 X^2  1 X^2+X+1 X^2+1  1 X^2+1 X^2+1 X+1  0
 0  0  0  1  1 X^2+X+1 X+1 X^3+X^2 X+1 X^3+1 X^2 X^3+X^2 X^3+X^2+X+1 X^2 X+1 X^2+1 X^3+X^2+X  X X^3+X X^3+X+1  1 X+1 X^3+X^2+X+1 X^3+X^2+1 X^2+X X^2+X+1 X^2+X X^2 X^3+X^2 X^3+X^2+X+1 X^3  X  X X^2+X X^3+X^2+1 X+1 X^3+X^2 X^3 X^2+X+1  1 X^3+X X^2+1 X^2+X+1 X^3+X+1  X X^2+X X^3+X^2 X^3+X+1 X^2+X+1 X+1 X^3+X^2+X+1  0  0  X X^2+1 X^3+X+1 X^3+X+1  0 X^3+X^2  1 X^3+X^2+1 X^3+X X^3+X+1 X^2+X+1 X^3  1  1 X^3+X^2  X  1 X^3+X^2+X X^3  0 X^3+X+1 X^2 X^3+X^2+1 X^2+X+1 X^3+X^2+X+1 X^2+X X^3+X^2+X X^3+X+1  0 X^2+X+1 X^2+1 X^3+X^2+1  X X^3+1  X X^3+X+1 X^3+X^2+1 X^3+X^2+1  0
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^2  0  0 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^3+X^2 X^3 X^3+X^2 X^3  0 X^3 X^3+X^2 X^3 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2  0 X^3+X^2 X^2 X^3 X^2  0 X^3  0 X^3+X^2  0 X^3 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3  0 X^3  0  0 X^3+X^2  0 X^3 X^2 X^3  0  0 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^2 X^3+X^2 X^2  0 X^2 X^2 X^3 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3  0

generates a code of length 92 over Z2[X]/(X^4) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+130x^82+798x^83+2299x^84+3994x^85+7217x^86+11030x^87+15042x^88+21430x^89+24824x^90+29404x^91+29663x^92+29914x^93+24940x^94+21912x^95+15205x^96+10340x^97+6390x^98+3690x^99+2219x^100+864x^101+501x^102+188x^103+40x^104+46x^105+24x^106+16x^107+11x^108+6x^110+2x^111+4x^113

The gray image is a linear code over GF(2) with n=736, k=18 and d=328.
This code was found by Heurico 1.16 in 868 seconds.