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  X  X  1  X X^3  0 X^2
 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  1 X^2+1 X^3+X^2+X  1  1  1
 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^3+X^2 X^3+X^2+X X^3+X^2  X 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+359x^74+324x^75+332x^76+252x^77+238x^78+180x^79+210x^80+52x^81+38x^82+24x^83+20x^84+8x^86+4x^88+4x^90+1x^98+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 5.22 seconds.