The generator matrix

 1  0  0  1  1  1  2  0  0  2  1  1  1  1  2  0  1  1  1  1  0  1  1  1  1  0  2  0  0  X X+2  X X+2 X+2  X X+2  X  X  1  1  1  1 X+2  1  1  1  1  1  1  1  1  1  1  1  1  2 X+2  X  2  X  X  2  2  X  1  1  1  1  X  0  1  1  1  1 X+2  X  0  2  0  1  1  1  1
 0  1  0  0  3  3  1 X+2  1  1  X X+3  X X+3  1  2  0 X+3  0 X+3  1  X  X  3  3  1  1  X  2  1  1  1  1  1  1  1  1  X  1  0 X+3 X+3  2  0 X+2  1  0 X+2 X+1  3  2  3  X X+1 X+2  X X+2  2  0 X+2  0  1  X X+2 X+2  2  2 X+2  2 X+2  1  3  1  3  1  1  1  1  1  1  X  2 X+3
 0  0  1 X+1 X+3  2 X+3  1 X+2  1  X  3  1 X+2 X+1  1 X+2 X+1  3  0  2  2 X+3  1  X X+2  1  1  1  X  3  2 X+1 X+2  1  2 X+1  1  1  2  X  1  1 X+3  3  0  X  0 X+3 X+2  3 X+3 X+3  2 X+2  0  1  1  1  1  1  2  1  1 X+2  2  0  X  1  1  X  2 X+2  0 X+2 X+2  X  X  0 X+2  X X+2  X
 0  0  0  2  2  0  2  2  2  0  2  0  0  2  0  2  0  0  2  2  2  2  0  2  0  0  2  2  0  0  0  0  0  2  2  2  2  0  0  2  0  2  0  0  2  2  2  0  2  2  0  0  2  0  0  2  2  2  2  0  2  2  0  2  2  0  0  2  0  0  2  2  2  2  0  0  2  2  0  0  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+423x^80+248x^82+120x^84+137x^88+72x^90+8x^92+12x^96+3x^104

The gray image is a code over GF(2) with n=332, k=10 and d=160.
This code was found by Heurico 1.16 in 45.3 seconds.