The generator matrix

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

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+33x^28+180x^30+84x^31+526x^32+360x^33+985x^34+984x^35+2262x^36+1640x^37+2273x^38+1632x^39+2278x^40+1016x^41+1006x^42+360x^43+465x^44+56x^45+154x^46+12x^47+59x^48+9x^50+8x^52+1x^54

The gray image is a code over GF(2) with n=152, k=14 and d=56.
This code was found by Heurico 1.16 in 6.32 seconds.