The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+408x^78+724x^80+877x^82+625x^84+504x^86+362x^88+294x^90+132x^92+104x^94+41x^96+17x^98+3x^100+4x^106

The gray image is a code over GF(2) with n=336, k=12 and d=156.
This code was found by Heurico 1.16 in 88.1 seconds.