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

generates a code of length 81 over Z4[X]/(X^2+2) 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 73.2 seconds.