The generator matrix

 1  0  0  1  1  1 X+2  1  2  1  1  X  1  2  1 X+2  1  1 X+2  1  0 X+2  1  1  X  1  X  1  1 X+2  2 X+2  1  1  X  1  1  1  2  2  1  1 X+2  1 X+2  1  1 X+2  X  1  1  1  1  1  1  1  1 X+2  0  1  X  2  1  X  1  1 X+2  1  X  0  X  1  1  1  2  1  1  1  1  2  1
 0  1  0  0  1 X+3  1  3  1  X X+1  1  X  2  X  1 X+3 X+2  1  1 X+2  1  X  3  1  0  X  2 X+3  1  1  1  X  X  2  3  1  0  2  1 X+1  2  1  3  0 X+2 X+2  1  1  3 X+1  0  1  0  2 X+3 X+3 X+2 X+2 X+3  1  1  2  1  2 X+3 X+2  1  1  1  1  0  X X+3  1  X  2  1 X+3  1  2
 0  0  1  1  1  0  1  X X+1 X+3  1 X+2  X  1 X+3  3  3 X+2  2  X  1 X+2  1 X+1 X+1  2  1 X+2  X  2 X+2  3  X X+3  1 X+3  0 X+2  1  0 X+2  1  3 X+1  1 X+2 X+3 X+1  3  0  0 X+2  3  1 X+1  X  1  1  1  1 X+2  1 X+3  1  2 X+3  1  0  X  3 X+2  1  2  1  1  X  0  3  X X+2  3
 0  0  0  X  0  0  2  0  2  X  2  2  0 X+2  0  X X+2 X+2 X+2  X  2 X+2  0 X+2 X+2  X  X  X X+2  2  X  0  2  X X+2  2 X+2 X+2  X  X  X  X  X  X  2 X+2  2  X  X  X  0 X+2 X+2  2  2  2 X+2  X  2  0  2  0 X+2  X  0  X X+2  0  X  0  2 X+2  X X+2  X X+2  2  X  0  X  2
 0  0  0  0  X X+2 X+2 X+2  X  0  X  2  2  0  0 X+2  X  2  0 X+2  0  0  2  X  X  2  2  2 X+2  2  2  2  X X+2 X+2  2  2  X  X  X  2  X  2  2  X X+2  0  0 X+2 X+2  0  2  X  X  2  2  2  X  2 X+2 X+2 X+2  0  X X+2  2 X+2  0  X X+2 X+2 X+2  2  X  2  X  X  0  X  0  0
 0  0  0  0  0  2  0  0  2  2  2  2  2  0  2  0  2  0  2  2  2  0  0  0  2  2  2  0  0  2  2  2  0  2  0  2  0  0  2  2  2  0  0  0  2  2  0  0  2  0  2  2  0  0  2  0  2  2  0  0  0  0  2  0  2  0  2  0  2  2  2  2  2  0  2  0  2  2  2  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+224x^72+268x^73+730x^74+620x^75+1084x^76+940x^77+1310x^78+1152x^79+1335x^80+1164x^81+1400x^82+1284x^83+1291x^84+912x^85+930x^86+536x^87+477x^88+224x^89+226x^90+56x^91+123x^92+12x^93+36x^94+35x^96+8x^98+6x^100

The gray image is a code over GF(2) with n=324, k=14 and d=144.
This code was found by Heurico 1.16 in 17.2 seconds.