The generator matrix

 1  0  1  1  1  0  1 X+2  1  2  1  1  X  1  1  1 X+2  1  1  2 X+2  1  1  1 X+2  1  1  1 X+2  1  2  1  1  1  1  1  1  X  1  X  1  X  1 X+2  1  1  1  1  1  X  1  1  2  2  X  2  1  0  1  1  1  2  1  0  1  1  1  X  1  1  1  0  1  X  1  1  1  X  2  1  1  1  2  X
 0  1  1  0 X+3  1  X  1 X+1  1  3 X+2  1  0  1  X  1 X+1  2  1  1 X+3 X+3 X+2  1  1  X  1  1  0  1  3  2  1  X X+1 X+3  1 X+3  1  1  1 X+2  1 X+3  0 X+2  1  0  1  1  3  1  1  1  1  3  1 X+1 X+1 X+1  1 X+3  0 X+3 X+3  1 X+2  3 X+3  X  1 X+2  0  1  2 X+2  1  1  2  2  1  1  0
 0  0  X  0 X+2  X  0  X X+2  X  X  0 X+2  X  2  X  2  2 X+2  0  0  X  2  X  0  2 X+2  0  0 X+2 X+2 X+2  X  2 X+2  2  X  0 X+2  2  2 X+2  0  X  0  0  2 X+2  2  X X+2  2  2  0 X+2  0  X  2 X+2  0  0 X+2 X+2  X  0  2  0 X+2  0  X  2  2  0 X+2  2  X  0  2  X  X  X X+2  0  2
 0  0  0  X  0  X  X  X  X  2 X+2  2  0  X  X  2  0  0  2 X+2 X+2  0  X  X  0  2  2  X  0 X+2  X  X  2  0  X  2  X  X  0  X X+2  X  2  0  0 X+2  X X+2  0  2  0  2 X+2  X  X  0  2  2  X X+2  X X+2  2  2  X  0  0 X+2  2  0  2  0  X  0 X+2 X+2  0  2  2  X  0  X  X  0
 0  0  0  0  2  2  2  0  2  2  0  2  0  0  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  2  0  2  2  2  0  0  0  2  0  0  0  2  0  2  2  2  0  2  2  0  2  0  2  2  0  2  2  2  0  0  2  0  0  0  0  2  0  0  0  0  2  0  0  0  2  0  2  0  0  2  2  0  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+214x^78+373x^80+330x^82+352x^84+276x^86+249x^88+144x^90+64x^92+16x^94+9x^96+10x^98+6x^100+2x^102+1x^108+1x^116

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 0.689 seconds.