The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  2  X  0  0  1  0  X  X  1  0  1  1  X  X  1  1  1
 0  X  0  0  0  0  0  0  0  X X+2  X  X X+2  X X+2  2 X+2  X  X  X  2  0  X  X  2  X  0 X+2  2  0 X+2 X+2  2  2  X  X  0
 0  0  X  0  0  0  X X+2  X  0  0  0  X  X X+2  X  2  2  0  2  X  2 X+2  2  X X+2  0  X X+2 X+2  2 X+2  0  2 X+2 X+2  0  0
 0  0  0  X  0  X  X X+2  0  X  X  2  0  2 X+2  X  X  X  2  X  X  X  X  2  X  X X+2  2  X  2  X X+2  X  2  X X+2  X  X
 0  0  0  0  X  X  0 X+2  X  2 X+2 X+2  0 X+2  X  0  2  2 X+2  X X+2 X+2  X  2  0  0 X+2 X+2  0  2  0  0  2  X  0  2  0  X
 0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  2  2  2  0  2  0  2  2  0  2  0  2  2  2  0  0  2  0  0  0  0  0
 0  0  0  0  0  0  2  0  2  2  0  2  0  0  2  2  2  0  0  0  0  2  2  2  0  2  0  2  0  0  0  2  2  0  2  0  2  0
 0  0  0  0  0  0  0  2  2  0  2  2  2  2  0  0  2  2  0  0  2  0  0  0  0  2  0  2  0  0  0  2  2  0  0  2  0  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+81x^28+98x^29+133x^30+286x^31+410x^32+574x^33+699x^34+1204x^35+1753x^36+1906x^37+2040x^38+1954x^39+1724x^40+1258x^41+808x^42+558x^43+314x^44+244x^45+135x^46+88x^47+65x^48+16x^49+21x^50+6x^51+3x^52+4x^54+1x^60

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 9 seconds.