The generator matrix

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

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+150x^80+100x^82+146x^84+88x^86+16x^88+4x^90+6x^92+1x^144

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 1.99 seconds.