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

generates a code of length 78 over Z2[X]/(X^4) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+362x^75+308x^76+366x^77+195x^78+236x^79+198x^80+242x^81+28x^82+94x^83+4x^84+4x^85+4x^87+4x^91+1x^108+1x^114

The gray image is a linear code over GF(2) with n=624, k=11 and d=300.
This code was found by Heurico 1.16 in 5.16 seconds.