The generator matrix

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

generates a code of length 70 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+286x^61+624x^62+1028x^63+1421x^64+1688x^65+2109x^66+2448x^67+2609x^68+2760x^69+3022x^70+2820x^71+2599x^72+2454x^73+2024x^74+1644x^75+1179x^76+824x^77+606x^78+328x^79+149x^80+82x^81+27x^82+20x^83+8x^84+2x^85+4x^86+2x^88

The gray image is a code over GF(2) with n=280, k=15 and d=122.
This code was found by Heurico 1.13 in 17.3 seconds.