The generator matrix

 1  0  0  1  1  1 X+2  X  1  1  1  X  1  2  1  1  X  1  1  X X+2  1  0  X  1  1  0  0  1  1  2  0  1  1  1  2  2 X+2
 0  1  0  0  3 X+1  1  2  0  0 X+3  1  1  1  3  X  1 X+2  2  1  1  1  X X+2 X+3 X+1  1  0  0  X  1  1  2 X+2  X  1  X  1
 0  0  1  1  3  2  3  1  2 X+1 X+3  2  2  1  1  1  2  X X+2 X+3  3  3  1  1  1 X+2  3  1  X  3 X+1  2  X  0 X+1  0 X+2 X+3
 0  0  0  X  X  0  X  X X+2  2  0 X+2  X  2 X+2  0  2  0 X+2  X  2  0  2  X X+2  2  X X+2  2 X+2  2 X+2  0  X  X  X 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+272x^34+148x^35+384x^36+148x^37+362x^38+96x^39+238x^40+64x^41+166x^42+44x^43+80x^44+12x^45+30x^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 12.1 seconds.