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

generates a code of length 83 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+277x^78+513x^80+424x^82+289x^84+215x^86+132x^88+87x^90+41x^92+44x^94+9x^96+9x^98+6x^100+1x^104

The gray image is a code over GF(2) with n=332, k=11 and d=156.
This code was found by Heurico 1.16 in 0.658 seconds.