The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+116x^72+64x^73+436x^74+256x^75+583x^76+392x^77+734x^78+528x^79+832x^80+636x^81+768x^82+468x^83+609x^84+384x^85+494x^86+280x^87+283x^88+60x^89+96x^90+4x^91+69x^92+56x^94+22x^96+8x^98+10x^100+2x^104+1x^108

The gray image is a code over GF(2) with n=324, k=13 and d=144.
This code was found by Heurico 1.16 in 5.94 seconds.