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

generates a code of length 83 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+189x^76+150x^78+414x^80+292x^82+455x^84+192x^86+170x^88+60x^90+79x^92+10x^94+21x^96+12x^100+2x^104+1x^132

The gray image is a code over GF(2) with n=332, k=11 and d=152.
This code was found by Heurico 1.16 in 14.3 seconds.