The generator matrix

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

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+72x^77+162x^78+204x^79+512x^80+402x^81+854x^82+604x^83+1207x^84+874x^85+1603x^86+1034x^87+1653x^88+924x^89+1610x^90+792x^91+1266x^92+558x^93+698x^94+330x^95+392x^96+196x^97+154x^98+78x^99+65x^100+40x^101+29x^102+24x^103+17x^104+6x^105+4x^106+6x^107+6x^108+4x^110+1x^112+2x^114

The gray image is a linear code over GF(2) with n=352, k=14 and d=154.
This code was found by Heurico 1.16 in 58.4 seconds.