The generator matrix

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

generates a code of length 94 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+64x^82+74x^83+212x^84+202x^85+469x^86+420x^87+820x^88+608x^89+1208x^90+816x^91+1526x^92+1008x^93+1657x^94+968x^95+1599x^96+810x^97+1270x^98+606x^99+739x^100+326x^101+341x^102+136x^103+170x^104+96x^105+81x^106+40x^107+36x^108+16x^109+17x^110+12x^111+8x^112+6x^113+8x^114+7x^116+2x^118+2x^120+1x^122+2x^126

The gray image is a linear code over GF(2) with n=376, k=14 and d=164.
This code was found by Heurico 1.16 in 25.3 seconds.