The generator matrix

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

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+59x^34+188x^35+298x^36+498x^37+622x^38+866x^39+637x^40+462x^41+191x^42+88x^43+84x^44+62x^45+23x^46+10x^47+4x^48+2x^49+1x^62

The gray image is a code over GF(2) with n=312, k=12 and d=136.
This code was found by Heurico 1.16 in 0.187 seconds.