The generator matrix

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

generates a code of length 84 over Z2[X]/(X^4) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+394x^75+1352x^76+3898x^77+6078x^78+10708x^79+14747x^80+21334x^81+25790x^82+31410x^83+30617x^84+32106x^85+25072x^86+22246x^87+14986x^88+10028x^89+5706x^90+3254x^91+1302x^92+576x^93+230x^94+166x^95+60x^96+50x^97+4x^98+10x^99+5x^100+8x^101+4x^103+2x^104

The gray image is a linear code over GF(2) with n=672, k=18 and d=300.
This code was found by Heurico 1.16 in 793 seconds.