The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+160x^67+225x^68+270x^69+184x^70+264x^71+195x^72+136x^73+107x^74+146x^75+76x^76+78x^77+44x^78+40x^79+46x^80+28x^81+15x^82+10x^83+1x^84+16x^85+2x^86+4x^87

The gray image is a code over GF(2) with n=288, k=11 and d=134.
This code was found by Heurico 1.16 in 0.426 seconds.