The generator matrix

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

generates a code of length 38 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+106x^31+379x^32+746x^33+1177x^34+1170x^35+1780x^36+1748x^37+2028x^38+1924x^39+1921x^40+1240x^41+1003x^42+602x^43+318x^44+116x^45+78x^46+22x^47+17x^48+6x^49+2x^50

The gray image is a code over GF(2) with n=152, k=14 and d=62.
This code was found by Heurico 1.13 in 2.21 seconds.