The generator matrix

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

generates a code of length 83 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+236x^77+317x^78+452x^79+354x^80+430x^81+365x^82+402x^83+241x^84+266x^85+176x^86+196x^87+146x^88+90x^89+109x^90+122x^91+53x^92+58x^93+21x^94+28x^95+5x^96+24x^97+4x^98

The gray image is a code over GF(2) with n=332, k=12 and d=154.
This code was found by Heurico 1.11 in 3.55 seconds.