The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+82x^77+220x^78+334x^79+375x^80+388x^81+373x^82+344x^83+313x^84+290x^85+268x^86+208x^87+229x^88+188x^89+109x^90+108x^91+81x^92+54x^93+47x^94+26x^95+23x^96+16x^97+2x^98+4x^99+2x^100+6x^101+5x^102

The gray image is a code over GF(2) with n=336, k=12 and d=154.
This code was found by Heurico 1.16 in 1.23 seconds.