The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+137x^30+261x^32+248x^34+240x^36+122x^38+8x^40+5x^46+2x^48

The gray image is a code over GF(2) with n=136, k=10 and d=60.
This code was found by Heurico 1.16 in 8.27 seconds.