The generator matrix

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

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+254x^78+272x^79+515x^80+328x^81+476x^82+248x^83+419x^84+256x^85+280x^86+168x^87+256x^88+128x^89+132x^90+56x^91+120x^92+48x^93+58x^94+24x^95+16x^96+8x^97+16x^98+13x^100+4x^104

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 1.51 seconds.