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

generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+26x^76+90x^77+85x^78+136x^79+147x^80+126x^81+172x^82+180x^83+194x^84+220x^85+187x^86+112x^87+108x^88+58x^89+41x^90+26x^91+23x^92+38x^93+20x^94+18x^95+11x^96+12x^97+7x^98+4x^99+1x^100+2x^103+2x^107+1x^136

The gray image is a code over GF(2) with n=336, k=11 and d=152.
This code was found by Heurico 1.16 in 0.814 seconds.