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

generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+153x^64+4x^65+445x^66+72x^67+586x^68+176x^69+624x^70+312x^71+917x^72+440x^73+904x^74+456x^75+805x^76+368x^77+670x^78+168x^79+398x^80+36x^81+299x^82+16x^83+171x^84+114x^86+35x^88+16x^90+5x^92+1x^100

The gray image is a linear code over GF(2) with n=296, k=13 and d=128.
This code was found by Heurico 1.16 in 6.79 seconds.