The generator matrix

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

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+246x^74+412x^75+930x^76+880x^77+1710x^78+1516x^79+2251x^80+2092x^81+2697x^82+2276x^83+2904x^84+2404x^85+2748x^86+2084x^87+2290x^88+1380x^89+1401x^90+760x^91+769x^92+396x^93+310x^94+112x^95+112x^96+16x^97+31x^98+8x^99+20x^100+8x^102+2x^104+1x^106+1x^108

The gray image is a linear code over GF(2) with n=336, k=15 and d=148.
This code was found by Heurico 1.16 in 60.3 seconds.