The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+172x^74+814x^75+1481x^76+2274x^77+2772x^78+3424x^79+3714x^80+4434x^81+3343x^82+3324x^83+2467x^84+1892x^85+1104x^86+764x^87+382x^88+162x^89+123x^90+30x^91+42x^92+22x^93+6x^94+12x^95+9x^96

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 14 seconds.