The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+100x^68+146x^69+178x^70+126x^71+155x^72+78x^73+42x^74+46x^75+14x^76+12x^77+46x^78+36x^79+20x^80+4x^81+4x^82+12x^84+2x^88+2x^90

The gray image is a code over GF(2) with n=288, k=10 and d=136.
This code was found by Heurico 1.11 in 0.189 seconds.