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

generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+67x^70+52x^71+31x^72+30x^73+48x^74+10x^75+8x^76+2x^77+1x^78+2x^79+4x^82

The gray image is a code over GF(2) with n=288, k=8 and d=140.
This code was found by Heurico 1.16 in 0.172 seconds.