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

generates a code of length 71 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+42x^68+32x^69+85x^70+192x^71+84x^72+32x^73+42x^74+1x^78+1x^136

The gray image is a code over GF(2) with n=284, k=9 and d=136.
This code was found by Heurico 1.16 in 67.9 seconds.