The generator matrix

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

generates a code of length 79 over Z2[X]/(X^4) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+266x^70+1156x^71+3403x^72+5780x^73+10013x^74+14854x^75+20731x^76+26646x^77+30892x^78+32924x^79+32746x^80+27738x^81+21183x^82+14152x^83+9351x^84+5346x^85+2763x^86+1136x^87+626x^88+242x^89+90x^90+56x^91+22x^92+8x^93+7x^94+6x^95+2x^98+2x^99+2x^103

The gray image is a linear code over GF(2) with n=632, k=18 and d=280.
This code was found by Heurico 1.16 in 694 seconds.