The generator matrix

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

generates a code of length 78 over Z2[X]/(X^4) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+194x^74+224x^75+118x^76+224x^77+524x^78+224x^79+118x^80+224x^81+194x^82+1x^92+1x^108+1x^112

The gray image is a linear code over GF(2) with n=624, k=11 and d=296.
This code was found by Heurico 1.16 in 0.375 seconds.