The generator matrix

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

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+292x^76+464x^78+429x^80+346x^82+192x^84+116x^86+103x^88+58x^90+19x^92+8x^94+19x^96+1x^100

The gray image is a code over GF(2) with n=324, k=11 and d=152.
This code was found by Heurico 1.16 in 0.498 seconds.