The generator matrix

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

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+170x^67+250x^68+212x^69+223x^70+226x^71+193x^72+138x^73+154x^74+98x^75+103x^76+84x^77+37x^78+42x^79+45x^80+22x^81+9x^82+24x^83+5x^84+8x^85+3x^88+1x^90

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 0.365 seconds.