The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+166x^64+176x^65+312x^66+204x^67+265x^68+132x^69+186x^70+104x^71+171x^72+84x^73+56x^74+20x^75+50x^76+20x^77+34x^78+24x^79+29x^80+4x^81+4x^82+5x^84+1x^88

The gray image is a code over GF(2) with n=276, k=11 and d=128.
This code was found by Heurico 1.11 in 0.221 seconds.