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

generates a code of length 81 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+149x^76+64x^78+357x^80+192x^82+190x^84+57x^88+13x^92+1x^152

The gray image is a code over GF(2) with n=324, k=10 and d=152.
This code was found by Heurico 1.16 in 3.38 seconds.