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

generates a code of length 81 over Z2[X]/(X^4) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+126x^75+804x^76+1192x^77+1653x^78+1876x^79+2100x^80+2016x^81+1731x^82+1486x^83+1146x^84+770x^85+686x^86+304x^87+218x^88+132x^89+94x^90+32x^91+10x^92+2x^93+2x^94+1x^96+1x^98+1x^102

The gray image is a linear code over GF(2) with n=648, k=14 and d=300.
This code was found by Heurico 1.16 in 5.64 seconds.