The generator matrix

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

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+76x^62+260x^63+404x^64+488x^65+572x^66+678x^67+660x^68+718x^69+818x^70+650x^71+565x^72+596x^73+545x^74+404x^75+245x^76+160x^77+147x^78+96x^79+32x^80+20x^81+13x^82+22x^83+11x^84+2x^85+3x^86+2x^87+2x^88+2x^90

The gray image is a code over GF(2) with n=280, k=13 and d=124.
This code was found by Heurico 1.16 in 3.39 seconds.