The generator matrix

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

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+52x^77+182x^78+168x^79+312x^80+184x^81+260x^82+112x^83+141x^84+64x^85+172x^86+74x^87+91x^88+48x^89+49x^90+24x^91+44x^92+32x^93+22x^94+6x^95+2x^96+4x^97+1x^98+1x^100+2x^102

The gray image is a code over GF(2) with n=332, k=11 and d=154.
This code was found by Heurico 1.16 in 0.509 seconds.