The generator matrix

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

generates a code of length 83 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+56x^77+139x^78+244x^79+265x^80+222x^81+198x^82+136x^83+122x^84+140x^85+121x^86+96x^87+78x^88+50x^89+50x^90+28x^91+19x^92+36x^93+18x^94+8x^95+10x^96+8x^97+2x^98+1x^100

The gray image is a code over GF(2) with n=332, k=11 and d=154.
This code was found by Heurico 1.11 in 0.385 seconds.