The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+362x^63+584x^64+1336x^65+999x^66+1986x^67+1693x^68+3146x^69+1915x^70+3396x^71+1985x^72+3650x^73+1965x^74+2976x^75+1587x^76+1990x^77+963x^78+1106x^79+392x^80+414x^81+168x^82+90x^83+28x^84+24x^85+4x^86+2x^88+4x^91+2x^94

The gray image is a code over GF(2) with n=288, k=15 and d=126.
This code was found by Heurico 1.13 in 18 seconds.