The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+115x^30+300x^32+16x^33+582x^34+160x^35+903x^36+496x^37+1182x^38+704x^39+1185x^40+496x^41+912x^42+160x^43+570x^44+16x^45+243x^46+103x^48+34x^50+7x^52+4x^54+3x^56

The gray image is a code over GF(2) with n=156, k=13 and d=60.
This code was found by Heurico 1.16 in 2.74 seconds.