The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  1  1  1  1  X  1  1  1  1  1  X  1  X  1  1  X  1  0 X^2  1  1  X  X  X  1  X
 0  X  0 X^2+X+2 X^2 X^2+X X^2+2  X  0 X^2+X  2 X^2+X X+2 X^2 X^2  X  0 X^2+X X^2 X+2  2 X+2  2 X+2 X^2+X  0 X+2 X^2  X  2 X^2+X  0 X^2  X  0 X^2+X+2 X^2+2 X^2+X+2 X+2  0  0 X^2+X+2 X^2+2 X^2+X  0 X^2+X X^2+2 X^2+X X^2+2 X^2 X+2 X^2+2  X  2 X^2+X+2 X^2+X  0 X+2 X^2+2 X^2 X^2+2 X^2+X X^2+X+2 X^2+X X^2+2  X X^2+2 X^2+X X^2+2  X X^2+X+2  2 X^2  X X^2 X+2 X^2+X X^2+X X^2+X+2  2 X^2+X
 0  0 X^2+2  0 X^2  0  2  0 X^2 X^2  2 X^2+2 X^2+2 X^2+2  0 X^2  0 X^2+2  2 X^2+2 X^2  2 X^2  0  0  0 X^2+2 X^2+2  0 X^2 X^2  2  2  2 X^2+2 X^2+2  2  2  0  0 X^2+2 X^2+2  0 X^2 X^2 X^2 X^2+2  2  2 X^2+2  0 X^2 X^2 X^2+2  0 X^2+2  2  2  2  0  2  2 X^2  2 X^2+2  2 X^2  2  0  2 X^2+2 X^2  2  0 X^2 X^2+2 X^2+2 X^2+2 X^2 X^2  2
 0  0  0 X^2+2  0  2  2 X^2 X^2 X^2 X^2  0  0 X^2 X^2+2 X^2  2 X^2+2 X^2+2  2  0 X^2+2 X^2+2  2  0 X^2+2 X^2 X^2+2 X^2+2  0  2  2  2 X^2+2 X^2+2 X^2 X^2+2 X^2  2  0  2  2 X^2 X^2+2 X^2+2  0  2  2  0 X^2+2  0  2  0 X^2 X^2 X^2+2 X^2+2  0 X^2 X^2+2 X^2 X^2+2 X^2+2 X^2+2 X^2 X^2+2  2  0  2  0  2 X^2 X^2 X^2+2 X^2 X^2+2 X^2  0 X^2+2  2  2
 0  0  0  0  2  2  2  2  0  0  0  2  0  2  2  2  0  0  2  0  0  2  0  0  2  0  2  2  0  2  2  2  0  0  0  0  0  2  2  2  0  0  2  2  2  2  2  0  0  0  2  0  2  2  2  2  2  0  2  0  0  2  0  0  0  0  2  2  0  2  2  2  2  2  2  2  0  0  2  2  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+160x^76+256x^77+209x^78+402x^79+539x^80+790x^81+557x^82+372x^83+208x^84+196x^85+47x^86+74x^87+44x^88+62x^89+18x^90+8x^91+4x^92+8x^93+4x^96+1x^138

The gray image is a code over GF(2) with n=648, k=12 and d=300.
This code was found by Heurico 1.16 in 73.4 seconds.