The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  0  1  1  1  X  2  1  1  1  1  0  1  1  1  1  X  X  1  1  2  0  1  0  1  1  1  1  2  1  X  1  0  1  1  X  1  1  1  1  X  1  1  1  1
 0  X  0  0  0  0  0  0  2  X X+2 X+2  X  X X+2 X+2  2  2  0  X  X X+2  X  0  X  X  0 X+2  X  2  2  2 X+2 X+2  0 X+2 X+2  X  2 X+2 X+2 X+2  X  2  X  0 X+2  0 X+2  0  2  X  X  0  X  X  0  0  2  0  2 X+2  0  2  X X+2 X+2  2  0  X X+2 X+2  X X+2  X X+2  2  0  0  0  X
 0  0  X  0  0  0  X X+2 X+2  X  X  2  X  X  2  0  2 X+2 X+2 X+2  0  X X+2 X+2  0 X+2 X+2  2  2  0  0  2  2 X+2  0 X+2 X+2 X+2  2  2 X+2  0  2  2 X+2  X  X  2  2  X  2  2  X X+2  X  X  2  X X+2  X  X X+2  0 X+2  2  X  X X+2  2  0  2  2 X+2  X X+2  0  0  0  0  X  0
 0  0  0  X  0  X  X  X  0  2  0  X X+2 X+2  X  2  2  0  0  0  2  2 X+2  X X+2  X  X  0  X  2 X+2 X+2 X+2  X X+2 X+2 X+2  X  X  0  2  2  2  0 X+2  2  2  2  2 X+2 X+2 X+2 X+2  0  0  X  X  X  X  X  0  X  X  X  X  0  2  2  0  0  0  0  X  X  2  0  X X+2  0  X  2
 0  0  0  0  X  X  2 X+2  X  2  X  0  X  0  X  X X+2 X+2  0  2  X  X  2  0  2 X+2 X+2  0  X  0  2  X X+2  X X+2  2 X+2  2  0  0  X  2  X  2  2  2  0  X  0  X  2  2  X  0 X+2  0  X  2  0 X+2  X  X  2 X+2 X+2  2  X  2  X  X  X  0  2  X  2 X+2  0  2  2  X X+2
 0  0  0  0  0  2  2  2  0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  2  0  2  2  2  2  0  0  0  2  2  2  0  0  0  2  0  2  0  0  2  0  0  2  2  2  2  2  2  2  2  0  0  2  2  0  2  2  0  2  0  0  0  2  0  2  0  2  2  2  0  0  0  0  0  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+111x^72+254x^74+20x^75+376x^76+108x^77+378x^78+244x^79+535x^80+300x^81+458x^82+220x^83+326x^84+100x^85+218x^86+28x^87+175x^88+4x^89+120x^90+54x^92+36x^94+18x^96+8x^98+3x^100+1x^132

The gray image is a code over GF(2) with n=324, k=12 and d=144.
This code was found by Heurico 1.16 in 1.86 seconds.