The generator matrix

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

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+67x^66+82x^67+89x^68+112x^69+52x^70+46x^71+14x^72+14x^73+11x^74+6x^76+2x^77+12x^78+1x^80+1x^84+2x^86

The gray image is a code over GF(2) with n=276, k=9 and d=132.
This code was found by Heurico 1.13 in 0.078 seconds.