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  1  1  1  1  1  1  1  1  1
 0 X^3  0  0  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0
 0  0 X^3  0  0  0  0  0  0  0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0  0  0  0  0  0  0
 0  0  0 X^3  0  0  0  0  0  0  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0
 0  0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0 X^3 X^3  0  0  0  0  0  0  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0  0  0  0 X^3  0 X^3  0  0  0  0  0  0
 0  0  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0  0  0  0  0  0

generates a code of length 70 over Z2[X]/(X^4) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+63x^64+896x^70+63x^76+1x^140

The gray image is a linear code over GF(2) with n=560, k=10 and d=256.
This code was found by Heurico 1.16 in 0.234 seconds.