The generator matrix

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

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+176x^71+438x^72+786x^73+1023x^74+1446x^75+1630x^76+2300x^77+2195x^78+2650x^79+2449x^80+2922x^81+2422x^82+2640x^83+2204x^84+2176x^85+1573x^86+1226x^87+900x^88+686x^89+375x^90+268x^91+110x^92+84x^93+22x^94+36x^95+12x^96+6x^97+4x^98+6x^99+1x^102+1x^110

The gray image is a linear code over GF(2) with n=324, k=15 and d=142.
This code was found by Heurico 1.16 in 55.2 seconds.