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

generates a code of length 77 over Z2[X]/(X^4) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+154x^73+686x^74+672x^75+596x^76+470x^77+498x^78+252x^79+246x^80+128x^81+136x^82+120x^83+91x^84+28x^85+15x^86+1x^90+2x^92

The gray image is a linear code over GF(2) with n=616, k=12 and d=292.
This code was found by Heurico 1.16 in 0.36 seconds.