The generator matrix

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

generates a code of length 78 over Z2[X]/(X^4) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+176x^69+1179x^70+3182x^71+5923x^72+9582x^73+15254x^74+20624x^75+26959x^76+30790x^77+33493x^78+31994x^79+28034x^80+20944x^81+15074x^82+8908x^83+5333x^84+2692x^85+1052x^86+472x^87+269x^88+146x^89+20x^90+16x^91+6x^92+6x^93+6x^94+4x^95+3x^96+2x^98

The gray image is a linear code over GF(2) with n=624, k=18 and d=276.
This code was found by Heurico 1.16 in 687 seconds.