The generator matrix

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

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+128x^74+732x^75+666x^76+596x^77+508x^78+392x^79+273x^80+248x^81+192x^82+156x^83+63x^84+84x^85+20x^86+32x^87+1x^88+3x^92+1x^96

The gray image is a linear code over GF(2) with n=624, k=12 and d=296.
This code was found by Heurico 1.16 in 0.36 seconds.