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

generates a code of length 69 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+20x^66+32x^67+47x^68+64x^69+36x^70+32x^71+15x^72+6x^74+1x^76+2x^98

The gray image is a code over GF(2) with n=276, k=8 and d=132.
This code was found by Heurico 1.16 in 23.9 seconds.