The generator matrix

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

generates a code of length 81 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+112x^74+718x^75+1593x^76+2262x^77+2722x^78+3698x^79+3576x^80+4090x^81+3757x^82+3220x^83+2535x^84+1960x^85+1087x^86+702x^87+367x^88+146x^89+88x^90+66x^91+21x^92+22x^93+9x^94+12x^95+2x^96+1x^98+1x^100

The gray image is a code over GF(2) with n=648, k=15 and d=296.
This code was found by Heurico 1.16 in 13.8 seconds.