The generator matrix

 1  0  0  1  1  1 X+2  1  2  1  1  X  1  0  1  1  2 X+2  1 X+2  1  2  1  X  2  1  1  0  2  1  1  1  2  1  1  1  1  2  1  0  0 X+2  1  1  1  1  1  1  2  1  X X+2  1  1  1  1  1 X+2  1  1  1  1  1  0 X+2  2 X+2  1  1  1  2  1
 0  1  0  0  1 X+3  1  3  1  X  2  X  3  1  2 X+3  0  1 X+1  1 X+2  1  X  2  1  1  0  1  1  1 X+3 X+2  0 X+2  1 X+3  0  1  X  1  1  X  1 X+2 X+3 X+3 X+2 X+3 X+2  2  2  1  2  3  3  2  3 X+2 X+3  1  1 X+1  2  1  1  1  1 X+2  1  2  2  1
 0  0  1  1  1  0  1  X X+1 X+3  X  1 X+3  X X+2  X  1 X+1  1  0 X+1  X  3  1 X+3 X+1  2  0  3  2 X+2 X+3  1  X X+3  3  1  1  0  3 X+2  1  X X+3 X+1  0  0  3  1 X+3  1 X+1  1  2  X  X  3  1  1 X+1  2  2  2  0  3  0  0  X  0  0  X  0
 0  0  0  X  0  0  2  0  2  X  0  0  0  0 X+2 X+2  X X+2 X+2 X+2  2 X+2  0  X X+2 X+2 X+2  2  X X+2  0  2  2  X X+2 X+2  2  X  X  2 X+2  0  X X+2  2  X  0  2 X+2  X  0  X  0 X+2  0  2  X  X  2  2  2 X+2  2 X+2  0  X X+2 X+2  0  X  2  0
 0  0  0  0  X X+2 X+2 X+2  X  0  0  2  X X+2  2 X+2  2  X  X  X  0  X  0  2 X+2 X+2  0  X X+2  0  0 X+2  X X+2  2  0  X  2 X+2  2  2 X+2  X  X  2  2  X  0 X+2  X  X  0 X+2  X  2  X  X  2 X+2 X+2  0  0 X+2  0 X+2  2 X+2  2  2  2  X X+2
 0  0  0  0  0  2  0  0  2  2  2  2  2  2  2  0  2  2  2  0  0  2  2  0  0  0  0  0  2  2  0  0  0  2  2  0  2  0  0  0  0  2  0  0  2  0  2  0  0  2  0  2  2  2  2  0  2  2  0  0  2  2  2  2  0  2  2  0  0  0  2  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+130x^63+326x^64+512x^65+745x^66+954x^67+977x^68+1164x^69+1335x^70+1428x^71+1451x^72+1290x^73+1362x^74+1236x^75+1050x^76+846x^77+576x^78+398x^79+249x^80+126x^81+67x^82+74x^83+37x^84+22x^85+9x^86+4x^87+5x^88+8x^89+2x^90

The gray image is a code over GF(2) with n=288, k=14 and d=126.
This code was found by Heurico 1.16 in 14.3 seconds.