The generator matrix

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

generates a code of length 71 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+124x^69+27x^70+16x^71+28x^72+24x^73+24x^77+4x^78+3x^80+4x^85+1x^86

The gray image is a code over GF(2) with n=284, k=8 and d=138.
This code was found by Heurico 1.16 in 52.1 seconds.