The generator matrix

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

generates a code of length 81 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+136x^75+764x^76+1196x^77+1740x^78+1920x^79+2111x^80+1796x^81+1676x^82+1476x^83+1348x^84+788x^85+644x^86+356x^87+217x^88+116x^89+50x^90+12x^91+10x^92+8x^93+8x^94+4x^95+5x^96+2x^98

The gray image is a code over GF(2) with n=648, k=14 and d=300.
This code was found by Heurico 1.16 in 3.63 seconds.