The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  0 X+2  1  1  1  0 X+2  1  1  1  1  1  0  1 X+2  1  1  1  1  0  0  1  1  1
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  0 X+1  1  1 X+2  0 X+2  1  1  3 X+1  3  0 X+2  1 X+1  1  3 X+1  0 X+2  1  1 X+1  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  0  2  2  2  2  0  0  0  0  0  0  0  2  0  2  2  2  0  2  0  2  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  0  0  2  2  2  0  2  0  2  2  0  2  0  2  0  2  0  0  2
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  0  2  2  2  2  2  2  0
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  0  0  0  0  0  2  2  2  2  0  0  0  2  2  2  0  2  2  0  2  0  0
 0  0  0  0  0  0  2  0  0  0  0  2  2  0  0  2  2  0  2  2  2  0  2  0  0  2  2  0  0  2  0  0  2  0  2  0  2  2
 0  0  0  0  0  0  0  2  0  0  2  0  0  0  2  2  0  2  2  2  2  2  0  2  2  2  0  2  2  2  0  2  2  2  0  0  0  0
 0  0  0  0  0  0  0  0  2  0  2  2  0  2  2  0  2  0  2  2  0  2  0  2  0  0  2  0  2  2  2  0  2  0  0  0  0  2
 0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  0  2  2  0  0  0  0  2  2  0  2  2  0  0  0  0  0  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+112x^28+36x^30+32x^31+533x^32+352x^33+688x^34+1312x^35+1919x^36+2400x^37+1624x^38+2400x^39+1923x^40+1312x^41+688x^42+352x^43+515x^44+32x^45+36x^46+101x^48+13x^52+1x^56+1x^60+1x^64

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 6.44 seconds.