The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+35x^28+108x^30+224x^32+306x^34+216x^36+90x^38+29x^40+6x^42+5x^44+2x^46+1x^48+1x^56

The gray image is a code over GF(2) with n=136, k=10 and d=56.
This code was found by Heurico 1.16 in 0.0525 seconds.