The generator matrix

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

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+289x^78+634x^79+1183x^80+1600x^81+2254x^82+2566x^83+3604x^84+3590x^85+4591x^86+4450x^87+5537x^88+4996x^89+5512x^90+4658x^91+4714x^92+3672x^93+3505x^94+2446x^95+2160x^96+1366x^97+932x^98+494x^99+360x^100+160x^101+127x^102+46x^103+39x^104+38x^105+6x^106+2x^107+2x^108+2x^109

The gray image is a linear code over GF(2) with n=356, k=16 and d=156.
This code was found by Heurico 1.13 in 75 seconds.