The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+372x^62+732x^63+1302x^64+1832x^65+2719x^66+3288x^67+3976x^68+4700x^69+5076x^70+5728x^71+5633x^72+6000x^73+5444x^74+4880x^75+4237x^76+3184x^77+2330x^78+1588x^79+1224x^80+632x^81+323x^82+168x^83+89x^84+36x^85+18x^86+14x^88+6x^90+2x^92+2x^96

The gray image is a code over GF(2) with n=288, k=16 and d=124.
This code was found by Heurico 1.13 in 70.1 seconds.