The generator matrix

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

generates a code of length 83 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+36x^80+170x^81+32x^82+64x^83+24x^84+144x^85+24x^86+2x^88+4x^89+6x^90+2x^97+1x^98+1x^112+1x^114

The gray image is a code over GF(2) with n=332, k=9 and d=160.
This code was found by Heurico 1.16 in 0.409 seconds.