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  2  1  1  1  1  1  2  1  1  1  1  0  1  1  X  X
 0  X  0  X  0  0  X  X  0  0  X  X  2  0 X+2 X+2  2 X+2  X  2  2  X  0 X+2  X  0  2 X+2  2 X+2  0  X X+2  2  0  0  2  X  X X+2  X  X  2  2  X  0 X+2  X  0 X+2  0  0 X+2  2  X  2  0  X X+2  X  2  2  2 X+2  2  0 X+2  2  X
 0  0  X  X  0 X+2  X  0 X+2  0  X  0  X  2  0  X  X  2  X  0 X+2 X+2  0  2  X  2 X+2  0  0 X+2  X  0  2  X  2  X  2  2  X  0  X  0  X  2 X+2  X X+2 X+2  2 X+2  2  2  2  0  2  X X+2 X+2 X+2  X X+2  0 X+2  0  0 X+2  2  X  X
 0  0  0  2  0  0  2  0  0  2  0  2  2  2  2  0  2  2  0  2  0  0  2  2  2  0  2  0  0  2  2  0  2  0  2  2  0  0  0  0  2  2  2  2  2  0  0  0  2  2  0  0  2  0  0  0  2  0  2  2  2  0  2  2  0  0  0  2  0
 0  0  0  0  2  0  2  2  2  2  0  0  2  0  2  2  0  0  0  2  2  2  0  2  2  2  2  2  0  0  0  0  0  0  2  0  2  0  2  2  0  2  2  0  2  2  0  0  2  2  0  0  2  0  0  0  0  2  0  2  0  2  2  0  0  0  2  0  0
 0  0  0  0  0  2  0  0  2  2  2  2  0  2  2  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  0  0  0  2  0  0  2  0  2  2  2  2  2  0  2  0  0  2  2  0  0  2  2  2  0  2  0  2  0  0  0  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+105x^64+108x^66+64x^67+235x^68+128x^69+182x^70+64x^71+27x^72+36x^74+29x^76+22x^78+18x^80+4x^82+1x^128

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 0.42 seconds.