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

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+79x^64+152x^65+71x^66+256x^67+16x^68+32x^69+16x^70+256x^71+8x^72+16x^73+8x^74+16x^76+32x^77+16x^78+8x^80+24x^81+16x^82+1x^130

The gray image is a code over GF(2) with n=276, k=10 and d=128.
This code was found by Heurico 1.16 in 0.291 seconds.