The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  X  1  1  1  0  0  1  1 X+2 X+2  1  1  1  1  1  1  0  1  1 X+2  1  1  X  1  1  X  1  1  2  1 X+2  0  1  1  1  1  2  1  1  1  0  2  1  1  1  1  X  0  0  1  1  1  1  1  X  1  1  1  1  1
 0  1  1 X+2 X+3  1  0 X+1  1  X  1  3  1 X+2  1  1  0 X+3  1  1  2 X+2 X+1  3 X+3  0  1 X+1  1  1 X+2  1  1  3 X+1  1 X+1  2  1  X  1  1  1  1  0 X+2  1  2  X  X  1  1 X+1  2 X+3  2  1  1  1  X X+3  3  3 X+1  2 X+2  1  0 X+2  0
 0  0  X  0 X+2  0 X+2  2  X  X X+2  0  X  2  0 X+2  0  X X+2  2  X  X  0  2  X  2  2  0  0  2  2 X+2  X  0 X+2  X  2 X+2  X X+2 X+2  X X+2 X+2  2  X  X  0 X+2  2  2  2  X  2  2 X+2  2  0  0  X  2 X+2 X+2  2 X+2  2  2  0  2  0
 0  0  0  2  0  0  0  2  2  0  0  0  0  0  0  2  2  0  0  0  2  2  2  2  2  0  2  2  0  2  0  2  2  0  0  2  2  0  2  2  0  0  0  2  2  2  2  0  2  0  0  0  2  2  0  0  2  0  2  2  2  2  0  0  2  2  0  0  2  0
 0  0  0  0  2  0  0  0  0  0  2  2  0  2  2  2  2  2  0  2  2  2  2  2  2  0  2  2  2  0  2  2  2  0  2  0  0  2  2  0  2  0  0  0  2  0  0  2  0  0  2  0  0  2  0  0  2  2  0  2  2  0  2  2  0  2  0  0  2  0
 0  0  0  0  0  2  0  0  0  2  0  2  0  0  0  0  0  0  0  2  0  2  0  0  2  2  0  2  2  2  2  2  2  0  2  2  2  2  2  2  2  2  2  0  2  0  0  0  2  0  0  2  2  2  0  2  2  2  2  0  2  2  0  0  0  0  2  2  0  0
 0  0  0  0  0  0  2  0  2  0  0  0  2  0  0  2  0  2  0  0  2  0  2  0  2  2  2  2  2  0  0  0  0  2  0  2  2  2  2  0  2  2  0  2  0  0  0  0  2  2  2  2  0  2  0  2  2  0  2  2  0  0  0  0  0  2  2  0  0  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+31x^62+98x^63+175x^64+264x^65+327x^66+322x^67+352x^68+370x^69+340x^70+356x^71+343x^72+306x^73+278x^74+216x^75+130x^76+74x^77+27x^78+18x^79+13x^80+6x^81+15x^82+14x^83+6x^84+4x^85+2x^86+3x^88+4x^90+1x^96

The gray image is a code over GF(2) with n=280, k=12 and d=124.
This code was found by Heurico 1.16 in 1.12 seconds.