The generator matrix

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

generates a code of length 79 over Z2[X]/(X^4) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+152x^73+639x^74+1400x^75+1578x^76+1906x^77+2080x^78+1840x^79+1710x^80+1596x^81+1280x^82+936x^83+562x^84+312x^85+137x^86+148x^87+57x^88+16x^89+12x^90+12x^91+2x^92+2x^93+3x^94+2x^96+1x^98

The gray image is a linear code over GF(2) with n=632, k=14 and d=292.
This code was found by Heurico 1.16 in 5.27 seconds.