The generator matrix

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

generates a code of length 77 over Z2[X]/(X^4) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+313x^74+392x^75+383x^76+148x^77+264x^78+220x^79+162x^80+32x^81+63x^82+32x^83+24x^84+4x^85+4x^88+4x^91+1x^100+1x^112

The gray image is a linear code over GF(2) with n=616, k=11 and d=296.
This code was found by Heurico 1.16 in 0.454 seconds.