The generator matrix

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

generates a code of length 38 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+342x^34+532x^36+468x^38+350x^40+216x^42+108x^44+28x^46+1x^48+2x^50

The gray image is a code over GF(2) with n=152, k=11 and d=68.
This code was found by Heurico 1.11 in 73.5 seconds.