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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+66x^76+114x^77+150x^78+198x^79+322x^80+346x^81+443x^82+474x^83+518x^84+592x^85+601x^86+780x^87+641x^88+538x^89+486x^90+448x^91+355x^92+258x^93+209x^94+154x^95+126x^96+102x^97+91x^98+54x^99+37x^100+28x^101+27x^102+4x^103+14x^104+6x^105+8x^106+1x^126

The gray image is a linear code over GF(2) with n=348, k=13 and d=152.
This code was found by Heurico 1.16 in 7.94 seconds.