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
 0  2  0  0  0  0  0  0  0  0  0  2  0  2  0  2  0  2  2  2  0  2  2  2  0  2  0  2  2  2  2  2  0  0
 0  0  2  0  0  0  0  0  0  0  2  0  2  0  2  0  2  2  2  0  2  2  2  0  2  2  2  2  2  2  0  0  0  0
 0  0  0  2  0  0  0  2  2  2  2  2  2  2  0  0  2  0  0  2  2  2  2  2  0  0  0  0  2  2  0  0  0  0
 0  0  0  0  2  0  2  2  2  0  0  0  0  0  0  0  2  0  2  2  2  2  0  2  2  0  2  2  2  0  2  2  0  0
 0  0  0  0  0  2  2  0  2  2  0  0  2  2  2  2  2  0  2  2  0  0  0  0  0  2  2  0  2  2  0  2  0  0

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+31x^32+192x^34+31x^36+1x^68

The gray image is a code over GF(2) with n=136, k=8 and d=64.
This code was found by Heurico 1.16 in 0.0137 seconds.