The generator matrix

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

generates a code of length 39 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+120x^34+772x^35+1206x^36+2160x^37+2333x^38+3242x^39+2625x^40+1992x^41+922x^42+684x^43+176x^44+100x^45+29x^46+6x^47+8x^48+4x^49+4x^50

The gray image is a code over GF(2) with n=312, k=14 and d=136.
This code was found by Heurico 1.16 in 1.38 seconds.