The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+106x^69+45x^70+94x^71+47x^72+100x^73+18x^74+64x^75+12x^76+18x^77+1x^78+1x^80+2x^87+2x^92+1x^96

The gray image is a code over GF(2) with n=288, k=9 and d=138.
This code was found by Heurico 1.16 in 2.02 seconds.