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

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+254x^77+178x^78+652x^79+194x^80+596x^81+212x^82+534x^83+158x^84+354x^85+112x^86+258x^87+47x^88+132x^89+57x^90+154x^91+44x^92+76x^93+16x^94+42x^95+4x^96+12x^97+1x^98+8x^99

The gray image is a code over GF(2) with n=332, k=12 and d=154.
This code was found by Heurico 1.16 in 1.73 seconds.