The generator matrix

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

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+322x^34+568x^36+448x^38+342x^40+236x^42+112x^44+16x^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 1.16 in 2.11 seconds.