The generator matrix

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

generates a code of length 81 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+266x^72+1358x^73+3278x^74+6098x^75+10544x^76+14658x^77+20889x^78+26394x^79+30720x^80+33338x^81+31697x^82+26212x^83+21120x^84+14882x^85+10177x^86+5434x^87+2671x^88+1312x^89+633x^90+298x^91+75x^92+46x^93+14x^94+8x^95+6x^96+4x^97+4x^99+5x^100+2x^101

The gray image is a code over GF(2) with n=648, k=18 and d=288.
This code was found by Heurico 1.16 in 696 seconds.