The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  X  X  X  2  1  0  1  2  1  0  2  0  X  1  X  1  X  0  1  1  2  1  1  2  0  1  1  1  1  1  1  X  1
 0  X  0  0  0  0  0  0  2  2  X X+2  X  0  0  2 X+2 X+2  X  X  X  X  0  X X+2  X  0  X X+2  2 X+2  2  2 X+2  X  0  0  X  2  2 X+2  2  X  X  2  X  X  X  2  0  2  2  X X+2 X+2 X+2  X X+2  2  X  X  0  2  2  2  0  X  0  2  X  X  0
 0  0  X  0  0  0  0  0  0  0  0  0  2 X+2 X+2 X+2  X X+2 X+2  X  2  2 X+2 X+2  0  0  X  X  X X+2 X+2 X+2  2  2 X+2  X  X  2  2  X  X  0  X  2  X  0 X+2  0  0  X  2  X X+2  2  2  2  0  2  2  X  2 X+2  2  X  2  2  X X+2  0  0  X X+2
 0  0  0  X  0  0  2 X+2  X  X  X  X  2 X+2  X  2  2  0  2  2  2  2  2  X X+2  X  2  X X+2 X+2  X X+2  0  2  0  0  0 X+2  2  X X+2  0  0  0  X  0  X  2  X  X  X  2  0  0  2  X  0 X+2  0 X+2  2 X+2  0 X+2  X  2  X  X X+2  X  0  2
 0  0  0  0  X  0 X+2 X+2  X  2 X+2 X+2  0  X  X  0  2  X  0 X+2 X+2  X X+2  X  2  2  X  2  2  0 X+2  2  0 X+2  X X+2  2  0  X  0  0  2  0  X  0  X  0  2  0  X X+2  2  2  2  2  X  2  X  2  2  0  X  X  0  2  X X+2  X  0  0  2  X
 0  0  0  0  0  X  X  2 X+2  X X+2  2  X  X  0  X  0 X+2 X+2  0  X  2  2 X+2  2  X X+2 X+2  2  X  2  2 X+2  0  X X+2  0  0  X  X  0 X+2  2  2  2 X+2  X X+2  2  X  2  X  X  X X+2  X  2 X+2  X X+2  2 X+2  2  0  2 X+2 X+2  X  X  X  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+144x^62+4x^63+387x^64+48x^65+486x^66+156x^67+746x^68+304x^69+900x^70+496x^71+1035x^72+524x^73+816x^74+332x^75+645x^76+136x^77+408x^78+36x^79+292x^80+12x^81+154x^82+72x^84+28x^86+21x^88+8x^90+1x^108

The gray image is a code over GF(2) with n=288, k=13 and d=124.
This code was found by Heurico 1.16 in 6.29 seconds.