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

generates a code of length 77 over Z2[X]/(X^4) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+18x^73+87x^74+122x^75+173x^76+244x^77+171x^78+100x^79+57x^80+26x^81+20x^82+2x^83+1x^84+1x^86+1x^130

The gray image is a linear code over GF(2) with n=616, k=10 and d=292.
This code was found by Heurico 1.16 in 0.375 seconds.