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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+129x^74+104x^76+310x^78+257x^80+136x^82+15x^84+58x^86+6x^88+7x^90+1x^148

The gray image is a linear code over GF(2) with n=316, k=10 and d=148.
This code was found by Heurico 1.16 in 1.38 seconds.