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

generates a code of length 71 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+328x^62+680x^63+976x^64+1416x^65+1784x^66+2032x^67+2380x^68+2608x^69+2682x^70+2952x^71+2922x^72+2752x^73+2338x^74+2012x^75+1686x^76+1128x^77+856x^78+584x^79+317x^80+184x^81+66x^82+28x^83+34x^84+8x^85+10x^86+4x^88

The gray image is a code over GF(2) with n=284, k=15 and d=124.
This code was found by Heurico 1.13 in 17.8 seconds.