The generator matrix

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

generates a code of length 71 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+301x^64+268x^65+708x^66+492x^67+915x^68+572x^69+760x^70+544x^71+872x^72+532x^73+608x^74+320x^75+424x^76+212x^77+274x^78+112x^79+190x^80+16x^81+48x^82+4x^83+17x^84+2x^86

The gray image is a code over GF(2) with n=284, k=13 and d=128.
This code was found by Heurico 1.16 in 3.23 seconds.