The generator matrix

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

generates a code of length 81 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+406x^73+1597x^74+3254x^75+5464x^76+8090x^77+10208x^78+13224x^79+15238x^80+16292x^81+15383x^82+13470x^83+10625x^84+7614x^85+4657x^86+2882x^87+1498x^88+666x^89+264x^90+126x^91+67x^92+20x^93+19x^94+2x^95+2x^96+2x^99+1x^104

The gray image is a code over GF(2) with n=648, k=17 and d=292.
This code was found by Heurico 1.16 in 201 seconds.