The generator matrix

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

generates a code of length 71 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+68x^63+197x^64+420x^65+563x^66+566x^67+620x^68+714x^69+759x^70+792x^71+726x^72+578x^73+553x^74+436x^75+357x^76+278x^77+191x^78+164x^79+65x^80+50x^81+40x^82+22x^83+15x^84+8x^85+2x^86+3x^88+4x^90

The gray image is a code over GF(2) with n=284, k=13 and d=126.
This code was found by Heurico 1.16 in 3.67 seconds.