The generator matrix

 1  0  0  1  1  1 X+2  1  1  0  X  1  1  X  1  1  X  X  1  1 X+2  1  1  X  1  2 X+2 X+2  1  1  1  0  2  1  1  1  1  1  0  1  1  2  1 X+2  1  X  1  2  1  0  1  1  2  1 X+2  0  1  1 X+2  0  1  2  0  1  1  1  0  0 X+2  1
 0  1  0  0  1 X+1  1 X+2  3  1  X  3 X+2  1 X+3  0  2  1 X+1  X  1 X+3  0  1  1  1  1  1 X+2  1  3  1  0  X X+1  X  X X+3  2  0 X+3  1  2 X+2  1  0 X+2  1  1  X X+2  X  1  1  1  1 X+2 X+1  1  1  1  1  X  0 X+1 X+2  1  2  1  0
 0  0  1  1  1  0  1  1  3  3  1  0  2  X  1  X  1 X+2 X+2  1 X+3  0  2  0 X+3 X+3  3  X X+3 X+1  X X+2  1  X  0 X+3 X+2  X  1  X  3 X+3 X+1  1  1  1  1  X X+1  1 X+3  1  0 X+3  0  3  3  1  3 X+1  2 X+2  1  1  3 X+3  3  1  0  0
 0  0  0  X  0  0  2  2 X+2  X  X  X  X X+2 X+2  2  0  0  0  2  0  X  X X+2  2  0  X  2 X+2  2  0  X  X X+2  X  0 X+2  X  2  0  0  X X+2  2  X X+2  X  2  0 X+2 X+2  0  2  X  X  0 X+2  X  X  2  2  0  X X+2  2  X  0 X+2  0  0
 0  0  0  0  X  2  X X+2  2  2 X+2 X+2  X X+2 X+2  X  X X+2 X+2  0  0  0  2  2  2 X+2  0  0 X+2  X  2  X  X  2 X+2  0  X  0  X  0 X+2  X  2  2  2 X+2 X+2  0  2  0  0 X+2  X  2  0  2 X+2  X X+2  2 X+2  0 X+2  0  0  X  0  2  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+73x^62+222x^63+425x^64+444x^65+738x^66+570x^67+766x^68+710x^69+794x^70+542x^71+666x^72+466x^73+581x^74+318x^75+358x^76+168x^77+126x^78+94x^79+52x^80+30x^81+21x^82+8x^83+4x^84+6x^85+3x^86+2x^87+4x^91

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 3.87 seconds.