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 X^2  1  1  1  1  1  1  1  1  1 X^3  1  1  1  1 X^2  1  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^2  0 X^3 X^2  0 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2  0  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^2  0  0 X^3 X^3+X^2 X^2 X^2 X^2  0 X^3 X^3 X^3 X^2 X^2  0  0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3  0  0 X^3 X^3+X^2 X^3+X^2
 0  0 X^3  0  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  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3  0  0 X^3  0 X^3  0
 0  0  0 X^3  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0  0  0  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3  0
 0  0  0  0 X^3  0  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3
 0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3  0  0 X^3
 0  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0

generates a code of length 67 over Z2[X]/(X^4) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+80x^62+206x^64+832x^66+784x^68+32x^70+16x^72+32x^74+16x^76+48x^78+1x^128

The gray image is a linear code over GF(2) with n=536, k=11 and d=248.
This code was found by Heurico 1.16 in 0.391 seconds.