The generator matrix

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

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+492x^74+1174x^76+1404x^78+1364x^80+1193x^82+979x^84+741x^86+451x^88+227x^90+123x^92+35x^94+4x^96+4x^98

The gray image is a linear code over GF(2) with n=324, k=13 and d=148.
This code was found by Heurico 1.11 in 119 seconds.