The generator matrix

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

generates a code of length 70 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+226x^63+340x^64+632x^65+661x^66+820x^67+599x^68+808x^69+573x^70+652x^71+510x^72+606x^73+514x^74+470x^75+217x^76+246x^77+91x^78+102x^79+59x^80+26x^81+13x^82+18x^83+2x^84+2x^85+2x^86+2x^90

The gray image is a code over GF(2) with n=280, k=13 and d=126.
This code was found by Heurico 1.16 in 3.02 seconds.