The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  1  1  0  1  1  1  1  X  0  X  1  0  1  1  1  X  X  X  X  1  1
 0  X  0 X+2  0 X+2  0 X+2  0 X+2  2 X+2  0 X+2 X+2  X X+2  0 X+2  X X+2  0  X  2 X+2  X X+2  0  X X+2  0 X+2 X+2  0 X+2 X+2  2 X+2
 0  0  2  0  0  0  0  0  0  0  2  0  2  0  0  0  2  0  0  2  2  2  2  2  0  0  2  2  0  0  2  0  2  0  0  2  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  0  0  2  2  2  0  2  0  2  2  2  2  0  2  0  0  2  2  0  2  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  2  0  0  2  2  2  2  0  2  2  0  0  2  2  2  0  2  2  0  0  2  0  2  2  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  0  0  2  0  0  0  0  2  2  0  0  2  2  2  0  2  2  2  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  2  0  2  2  2  2  0  0  2  2  2  2  0  0  0  0  2  2  2  0  2  0  2  0
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  0  2  2  0  2  2  2  0  2  2  2  2  0  0  2  0  2  0  2  2  2
 0  0  0  0  0  0  0  0  2  0  2  0  2  0  2  2  0  0  0  0  2  2  2  2  2  0  0  0  0  0  0  2  2  2  0  0  2  0
 0  0  0  0  0  0  0  0  0  2  0  2  0  0  2  0  2  2  0  0  2  2  2  0  0  2  0  0  2  0  0  0  2  2  0  2  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+116x^28+76x^30+16x^31+400x^32+112x^33+512x^34+336x^35+1292x^36+560x^37+1368x^38+560x^39+1262x^40+336x^41+544x^42+112x^43+396x^44+16x^45+60x^46+94x^48+20x^52+2x^56+1x^64

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 2.69 seconds.