The generator matrix

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

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+23x^64+118x^65+116x^66+102x^67+210x^68+146x^69+42x^70+40x^71+16x^72+68x^73+92x^74+16x^75+12x^77+3x^80+6x^81+3x^82+2x^83+2x^84+2x^85+2x^86+1x^96+1x^98

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 0.249 seconds.