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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+99x^66+295x^68+552x^70+1001x^72+1562x^74+2128x^76+2519x^78+2609x^80+2299x^82+1521x^84+867x^86+492x^88+222x^90+110x^92+58x^94+24x^96+8x^98+10x^100+3x^102+1x^104+2x^106+1x^110

The gray image is a linear code over GF(2) with n=316, k=14 and d=132.
This code was found by Heurico 1.16 in 29.9 seconds.