The generator matrix

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

generates a code of length 77 over Z2[X]/(X^4) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+162x^68+1352x^69+2927x^70+5888x^71+9247x^72+14842x^73+20623x^74+27060x^75+32029x^76+33460x^77+32066x^78+27858x^79+21139x^80+14914x^81+8873x^82+5196x^83+2449x^84+1194x^85+409x^86+266x^87+83x^88+44x^89+28x^90+12x^91+6x^92+2x^93+8x^95+4x^96+2x^98

The gray image is a linear code over GF(2) with n=616, k=18 and d=272.
This code was found by Heurico 1.16 in 675 seconds.