The generator matrix

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

generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+176x^74+475x^76+48x^77+769x^78+164x^79+1076x^80+340x^81+1370x^82+624x^83+1590x^84+944x^85+1626x^86+808x^87+1541x^88+552x^89+1377x^90+400x^91+863x^92+160x^93+639x^94+52x^95+339x^96+4x^97+262x^98+111x^100+46x^102+19x^104+7x^106+1x^116

The gray image is a linear code over GF(2) with n=344, k=14 and d=148.
This code was found by Heurico 1.16 in 30.6 seconds.