The generator matrix

1 0 0 0 0 0 0 1 1 1 X 1 1 0 1 1 0 1 1 X X 1 0 1 0 X 1 1 0 0 0 1 0 1 1 1 X 0 0 1 1 X 1 X 0 X 1 0 1 1 X 1 1 0 1 1 X X 1 1 X 1 0 0 1 0 0 1 1 0 X X 1 1 1 0 1 1 X X 1 1 X X 1 1 0 1 1 X 0 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 X X X 1 X+1 1 1 1 1 X+1 1 1 X+1 1 1 1 X 1 X 1 0 X+1 X 1 1 1 X 1 0 1 X 1 X+1 0 X 0 X X+1 0 X 1 X+1 1 X 1 0 1 0 1 X 1 1 X X+1 1 X X 1 X 0 1 X X+1 1 X 1 1 1 1 1 X+1 X 1 1 X X 0 1
0 0 1 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 0 0 X X X X 0 X X X 0 0 X X X 1 1 1 1 X+1 1 X+1 X+1 1 1 1 X+1 1 X+1 X+1 1 1 X+1 1 1 1 1 1 X+1 X 0 0 1 X 1 X+1 0 1 X X 1 0 X+1 1 1 1 0 0 X X X+1 X X 1 X X+1 X 0 1 1 1 0
0 0 0 1 0 0 0 0 0 X X 1 1 1 1 X+1 1 1 1 X+1 1 0 0 X X+1 0 X+1 X 0 1 1 X 1 1 X+1 1 X+1 0 X 0 0 0 X+1 1 X 0 1 X 0 1 0 X+1 X X+1 X 0 X X 0 X 1 X+1 1 X 1 1 1 0 0 0 0 X X+1 1 X+1 1 X 0 X 0 1 0 1 0 X X 1 X 1 1 X 1
0 0 0 0 1 0 0 1 X 1 1 0 X+1 1 0 1 0 X X X 0 1 X+1 X+1 1 X+1 X+1 0 0 1 X+1 X X X+1 1 1 1 X X+1 0 X 1 0 0 X+1 0 X X 1 X+1 X+1 X+1 1 X+1 1 X+1 X+1 X X 0 X+1 X+1 0 1 1 1 1 X X 1 1 X+1 X+1 X+1 1 1 X+1 X 1 X 1 X X X X X 0 X+1 1 1 X 0
0 0 0 0 0 1 0 1 X+1 0 1 X X+1 1 1 0 1 X 1 1 0 X 0 X+1 1 1 X+1 X X+1 0 X X+1 X 0 X+1 X X+1 X X X 1 1 1 X X+1 0 X+1 X+1 X 1 1 1 X+1 X X X 0 X+1 X+1 X+1 0 0 X+1 0 X+1 1 0 X+1 X X+1 1 X X+1 X 0 X+1 1 X X+1 X+1 0 X+1 1 X 0 1 X+1 0 0 1 X+1 0
0 0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 0 X X+1 X 1 0 X+1 0 1 1 1 0 X X+1 X+1 X 1 0 0 X+1 X+1 0 X+1 X+1 0 0 X 1 1 X X 1 X X+1 X X 0 1 X+1 X 1 X+1 X+1 X 0 X 1 X+1 0 X+1 X X+1 0 0 0 X 1 1 1 0 1 0 X+1 1 X 1 1 X X+1 X+1 0 0 0 1 X+1 0 1 1

generates a code of length 92 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+156x^78+584x^80+874x^82+1160x^84+1426x^86+1583x^88+1630x^90+1732x^92+1640x^94+1534x^96+1398x^98+983x^100+814x^102+493x^104+222x^106+108x^108+28x^110+13x^112+4x^114+1x^132

The gray image is a linear code over GF(2) with n=184, k=14 and d=78.
This code was found by Heurico 1.10 in 17.7 seconds.