The generator matrix

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

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+88x^69+30x^70+128x^71+62x^72+112x^73+32x^74+56x^77+1x^80+1x^94+1x^110

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 0.445 seconds.