The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+336x^80+64x^82+272x^84+64x^86+244x^88+32x^92+8x^96+2x^112+1x^128

The gray image is a code over GF(2) with n=336, k=10 and d=160.
This code was found by Heurico 1.16 in 19.4 seconds.