The generator matrix

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

generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+84x^73+183x^74+306x^75+414x^76+464x^77+497x^78+562x^79+634x^80+652x^81+733x^82+700x^83+659x^84+574x^85+444x^86+410x^87+274x^88+180x^89+137x^90+76x^91+55x^92+44x^93+34x^94+20x^95+10x^96+12x^97+18x^98+6x^99+6x^101+1x^102+1x^104+1x^106

The gray image is a linear code over GF(2) with n=328, k=13 and d=146.
This code was found by Heurico 1.16 in 6.34 seconds.