The generator matrix

 1  0  1  1  1 X+2  1  1  X  1  1  2 X+2  1 X+2  1  1  1  0  1  1  1  1  2  2 X+2  2  X  0 X+2  0 X+2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  X  1  1  1  1  0  X  1  1  1 X+2  X X+2  1  1  1  2  X  1  0  1  1  X  1 X+2  1  2  0  1  X  X
 0  1  1 X+2 X+3  1  2 X+1  1  X  3  1  1  0  1 X+1  0 X+1  1  X  1  X  1  1  1  1  1  1  1  1  1  1  0 X+2  2  X X+1  3  0 X+2  2  X X+3  1  1 X+3 X+1  3  0 X+3  1 X+3 X+2  3  3  2  3  1  0 X+3  X  0  1  1  1  X  X  0  1  1 X+2  X X+3 X+3  1  1  1  1  1  1 X+3  1  1
 0  0  X  0 X+2  0  X  2  X X+2  0 X+2  2  2  X  2  X  X  2 X+2 X+2  2  0 X+2  0  0  X  X  0  0  X  X  0  0  X  X  2  2  0  0  X  X  X X+2  X X+2  0  0  X  2  2  2 X+2  2 X+2  0 X+2  0  X X+2  X  X X+2  X X+2  0  0  2  0  2  2 X+2 X+2 X+2  2  0  2  2  2  0  0 X+2 X+2
 0  0  0  2  0  0  0  2  2  0  2  0  0  2  2  0  2  2  2  2  2  0  0  0  2  2  0  2  0  2  0  2  0  0  0  2  2  0  2  2  0  2  0  2  2  0  0  0  0  2  2  2  0  0  0  0  2  2  2  0  0  0  0  0  0  2  0  2  2  0  2  0  0  2  0  2  2  2  2  0  2  0  2
 0  0  0  0  2  0  0  0  0  2  2  0  2  2  2  0  2  2  2  0  0  2  2  2  0  2  0  2  2  0  2  0  0  2  2  2  2  0  0  2  0  0  0  2  0  2  2  0  0  0  2  0  2  2  2  2  2  2  0  0  0  2  0  2  0  2  0  0  0  0  0  2  0  0  0  2  0  0  2  2  0  0  2
 0  0  0  0  0  2  2  2  0  2  2  0  2  0  0  2  2  0  2  2  0  0  2  0  2  0  2  2  0  0  2  2  2  2  0  0  2  2  2  2  0  0  2  2  2  2  0  0  0  0  0  2  0  2  0  2  0  0  0  2  2  2  2  2  0  0  0  0  0  0  0  2  0  0  2  0  2  0  0  2  0  2  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+104x^77+187x^78+198x^79+173x^80+182x^81+226x^82+168x^83+165x^84+114x^85+83x^86+104x^87+79x^88+96x^89+65x^90+34x^91+27x^92+10x^93+8x^94+6x^95+2x^96+6x^97+5x^98+2x^99+2x^102+1x^112

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 3.91 seconds.