The generator matrix

 1  0  1  1  1 X+2  1  1  X  1  1  2 X+2  1 X+2  1  1  1  0  1  1  1  1  2  2 X+2  2  X  0 X+2  2  X  1  1  1  1  1  1  1  1  1  1  2  X  1  2  X  2  1  1  X  1  1  1  X  2  1  1  X  1  1 X+2  X  X  1  2  0  1  1  1  1  1  1  1  1  1  0  0  1  0  1  0  1  1
 0  1  1 X+2 X+3  1  2 X+1  1  X  3  1  1  0  1 X+1  0 X+1  1  X  1  X  1  1  1  1  1  1  1  1  1  1  0 X+2  2  X X+1  3  0 X+2  0 X+2  1  1  3  1  1  1  2  1  1  2 X+3  0  1  1 X+3  0  1  X  3  1  1  1  1  1  1  X X+1  X  0  0 X+1 X+1 X+2  2  2  1  1  1  1  0  1  2
 0  0  X  0 X+2  0  X  2  X X+2  0 X+2  2  2  X  2  X  X  2 X+2 X+2  2  0 X+2  0  0  X  X  0  0  X  X  0  0  X  X  2  2  0  0  X  X  0  0  2 X+2 X+2  0 X+2 X+2  2  X X+2 X+2  2  2  0  2  X  X X+2 X+2  2  X  X  X  0  2  2  0  0  X X+2 X+2  0  2  X  X  0  X  2  X  0  X
 0  0  0  2  0  0  0  2  2  0  2  0  0  2  2  0  2  2  2  2  2  0  0  0  2  2  0  2  2  0  2  0  0  0  0  0  2  2  2  2  2  2  2  0  0  2  0  0  2  2  2  0  2  2  2  0  0  2  2  0  2  0  2  0  0  2  0  0  2  2  2  0  0  2  2  0  0  2  0  0  2  2  0  0
 0  0  0  0  2  0  0  0  0  2  2  0  2  2  2  0  2  2  2  0  0  2  2  2  0  2  0  0  0  2  2  2  0  2  2  0  2  0  2  0  0  2  2  0  2  0  0  2  0  2  2  2  2  2  0  2  2  0  2  0  0  0  0  2  0  0  0  0  2  2  0  0  0  0  2  2  0  0  2  2  2  0  0  0
 0  0  0  0  0  2  2  2  0  2  2  0  2  0  0  2  2  0  2  2  0  0  2  0  2  0  2  2  0  0  2  2  2  2  0  0  2  2  2  2  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  0  0  0  2  2  2  0  0  0  2  2  2  2  0  0  2  0  2  2  2  0  2  0  0  0  0  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+199x^78+423x^80+343x^82+251x^84+261x^86+339x^88+149x^90+31x^92+26x^94+8x^96+12x^98+1x^100+2x^102+1x^108+1x^120

The gray image is a code over GF(2) with n=336, k=11 and d=156.
This code was found by Heurico 1.16 in 0.698 seconds.