The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+337x^66+740x^68+834x^70+686x^72+601x^74+359x^76+257x^78+180x^80+72x^82+17x^84+9x^86+1x^88+2x^90

The gray image is a code over GF(2) with n=288, k=12 and d=132.
This code was found by Heurico 1.16 in 8.11 seconds.