The generator matrix

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

generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+49x^74+146x^75+244x^76+248x^77+304x^78+338x^79+303x^80+360x^81+291x^82+306x^83+305x^84+278x^85+320x^86+196x^87+136x^88+104x^89+47x^90+34x^91+17x^92+24x^93+6x^94+2x^95+8x^96+8x^97+3x^98+2x^99+9x^100+2x^101+2x^102+2x^106+1x^108

The gray image is a linear code over GF(2) with n=328, k=12 and d=148.
This code was found by Heurico 1.16 in 1.5 seconds.