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

generates a code of length 69 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+45x^68+64x^69+15x^72+1x^76+2x^100

The gray image is a code over GF(2) with n=276, k=7 and d=136.
This code was found by Heurico 1.16 in 2.38 seconds.