The generator matrix

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

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+222x^74+420x^75+853x^76+1036x^77+1614x^78+1584x^79+2154x^80+2228x^81+2581x^82+2496x^83+2739x^84+2492x^85+2707x^86+2148x^87+1959x^88+1456x^89+1363x^90+980x^91+754x^92+368x^93+299x^94+116x^95+102x^96+36x^97+38x^98+10x^100+8x^102+4x^104

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 59.3 seconds.