The generator matrix

 1  0  0  0  1  1  1  2  0  1  1  1  0  1  0  2  1  X  X  1  X  1  1 X+2  1  0  1  X  1  1  1  1  X  1  1  1  1  1  1 X+2  1  X  1  0  1  2  2  1  2  1  1  1 X+2  1 X+2  0 X+2  1  1  1 X+2  0  1  0 X+2  1 X+2  1  2  X  1  1
 0  1  0  0  0  1  1  1  2  0  2  1  1  3  1  1  X  X  1  3  2 X+1 X+2  1  3  1  X X+2  X X+3 X+3  X  0  1  2  2  2 X+3  2  0  X  1  X  1 X+3  1  2  3  X  3  3 X+1  1 X+3  1 X+2  1  2  2 X+3  1  1  0 X+2  1 X+3 X+2  0  1  1 X+1  1
 0  0  1  0  1  2  3  1  1  2  1  1  2  2  3 X+1 X+3  1  2  0  0  0 X+3 X+2  3  1 X+2  1  2 X+3  1  0  X  X X+1 X+2  3  3  X  1 X+1  1  3  X  X X+3  1  2  1 X+2 X+3 X+3  1  1  1  1  0 X+3  1 X+2 X+3 X+3 X+3 X+2 X+2  2  1 X+1 X+3  0  3  0
 0  0  0  1  2  0  2  2  1  1  3  1  3  3  1  X X+2 X+2  X X+2  1  3 X+3  1  X X+3 X+1  0  X X+1  X X+3  1 X+1 X+3  1 X+1  3  2  1  1 X+2  0  3  0 X+1 X+1 X+3  X  X X+1  1  2 X+1  3  2 X+3  X X+2 X+2  X  1 X+2  1  2  2  0  2  1  2  2 X+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+168x^66+284x^67+421x^68+460x^69+432x^70+352x^71+372x^72+300x^73+304x^74+204x^75+164x^76+136x^77+172x^78+92x^79+80x^80+60x^81+36x^82+24x^83+21x^84+4x^85+4x^87+5x^88

The gray image is a code over GF(2) with n=288, k=12 and d=132.
This code was found by Heurico 1.11 in 0.429 seconds.