The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+48x^34+212x^35+180x^36+360x^37+178x^38+278x^39+168x^40+194x^41+107x^42+136x^43+64x^44+84x^45+16x^46+14x^47+3x^48+2x^49+2x^54+1x^58

The gray image is a code over GF(2) with n=156, k=11 and d=68.
This code was found by Heurico 1.16 in 0.107 seconds.