The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  X  1  1  2  1  2  1  1 X+2  1  1  1  1 X+2  1  1  2  1  X  1  0  1  1  1  1  2  X  1  1  1 X+2  1  1  0  1  1  0  1  1  1  1  X  1  1  X  X  1  1  X  1  2  1  2  2  1  1  1  X  1  1
 0  1  1  0  1  1  X X+3  1  1  1 X+2 X+1  1  2  1  1 X+2  1  0 X+1 X+2 X+1  1  3  0  1  1  1  0  1  0  2  3  1  1  1  3  3  X  1  2 X+3  1  3 X+3  1  0  2 X+1  0  1  X  1  1  1  1 X+3  1  3  1  1  1  1 X+2 X+2 X+2  1  X  3
 0  0  X  0  0  0  0  0  0  2  2  0  0  X X+2 X+2  X  X  X  X X+2  X  X  X  0  2  2  X X+2  X  2  0  2  X  0  2 X+2  2 X+2  X X+2  X  0  2  X  0  2 X+2 X+2  X  0 X+2 X+2 X+2  2  2 X+2  0  2  2  0  2 X+2 X+2 X+2  2  X  X  0  2
 0  0  0  X  0  0  X  X  X X+2  X  2  0  2  0  X  X  X  2  X  0  0 X+2 X+2  0  2  0 X+2  X  2  X  2 X+2  0  X  0  0  2  X  2  0  X  0  0  2 X+2  2 X+2  2  X  X  0  0 X+2 X+2 X+2  0  X  2  0  2 X+2  2  0  2  0 X+2  X  X  X
 0  0  0  0  X  0  0  2  2  0  2  2  2  2  2  0  0  0  2  2  2  2  0  2  2  0 X+2  X X+2  X X+2  X X+2 X+2 X+2 X+2 X+2  X X+2 X+2  2 X+2  X  2  X X+2 X+2 X+2  0 X+2  X  2 X+2  0  0 X+2 X+2 X+2  0  X  X  0  2  X  0  X  0  X  2  0
 0  0  0  0  0  2  2  2  2  0  0  2  2  2  0  0  0  2  0  0  2  2  2  2  0  0  0  0  2  2  2  2  2  2  2  2  0  2  0  0  2  0  0  2  0  0  2  0  2  2  0  0  0  2  2  0  2  2  0  2  0  2  0  0  0  2  0  2  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+196x^62+108x^63+444x^64+332x^65+790x^66+468x^67+809x^68+628x^69+842x^70+628x^71+759x^72+468x^73+662x^74+332x^75+315x^76+108x^77+128x^78+105x^80+32x^82+26x^84+6x^86+2x^88+2x^92+1x^96

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 20.8 seconds.