The generator matrix

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

generates a code of length 38 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+28x^28+50x^29+71x^30+168x^31+182x^32+284x^33+408x^34+580x^35+820x^36+948x^37+1100x^38+960x^39+808x^40+648x^41+404x^42+280x^43+176x^44+106x^45+51x^46+56x^47+23x^48+12x^49+12x^50+4x^51+8x^52+2x^54+2x^56

The gray image is a code over GF(2) with n=152, k=13 and d=56.
This code was found by Heurico 1.16 in 2.56 seconds.