The generator matrix

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

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+158x^62+48x^63+473x^64+244x^65+808x^66+532x^67+1308x^68+992x^69+1570x^70+1236x^71+1781x^72+1236x^73+1582x^74+1048x^75+1181x^76+568x^77+702x^78+196x^79+362x^80+32x^81+154x^82+12x^83+93x^84+46x^86+14x^88+4x^90+2x^92+1x^96

The gray image is a code over GF(2) with n=288, k=14 and d=124.
This code was found by Heurico 1.16 in 17.9 seconds.