The generator matrix

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

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+172x^66+280x^67+421x^68+436x^69+432x^70+396x^71+374x^72+284x^73+304x^74+212x^75+142x^76+140x^77+172x^78+76x^79+102x^80+68x^81+32x^82+20x^83+19x^84+8x^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 1.16 in 0.802 seconds.