The generator matrix

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

generates a code of length 70 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+288x^62+480x^63+837x^64+896x^65+1184x^66+1280x^67+1378x^68+1248x^69+1460x^70+1280x^71+1497x^72+1172x^73+966x^74+804x^75+639x^76+312x^77+270x^78+184x^79+117x^80+20x^81+52x^82+4x^83+7x^84+2x^86+4x^88+2x^90

The gray image is a code over GF(2) with n=280, k=14 and d=124.
This code was found by Heurico 1.16 in 13.9 seconds.