The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+278x^79+130x^80+280x^81+94x^82+386x^83+115x^84+174x^85+64x^86+180x^87+55x^88+76x^89+30x^90+82x^91+12x^92+34x^93+4x^94+18x^95+2x^96+8x^97+8x^99+4x^101+8x^103+4x^104+1x^108

The gray image is a code over GF(2) with n=336, k=11 and d=158.
This code was found by Heurico 1.16 in 90.6 seconds.