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  1  1  1  0  1  2  1  2  1  1  1  1  1  1  1  X  1  2  1  1  0  1  0  1  X  1  1  0  1  1  1  1  2  1  1  X  1  X  0  X  1  X  1  1
 0  X  0  0  0  0  0  2  2  X X+2  X  X  X X+2  X  0 X+2  2  X  2  X  0  X  2 X+2  X  0 X+2  2 X+2  0  0  2  0  X  X X+2  2  2 X+2  0  0  2 X+2  X  X  0  X  0  2  X X+2 X+2  0  X X+2  2  2  0  0 X+2  0  2  X  0 X+2  X X+2 X+2  2 X+2  0  X  2  0  2  X  2  0  2  0  2  0
 0  0  X  0  0  2 X+2  X  X  X  X  X X+2  0  0  0  2  2 X+2  X  2  0  0 X+2  2  2  X X+2  0  X  X X+2  X X+2 X+2  0  2  0  0  2 X+2  2  X  X  X  2  X  0  2  0  0 X+2  0  X  2  2  2  X X+2  X  0 X+2  X  X X+2 X+2  2 X+2 X+2  X X+2  0  X X+2 X+2 X+2  X  X  2 X+2  X  X X+2  0
 0  0  0  X  0 X+2 X+2  X  2 X+2 X+2  0  0  X  X  2  X  2 X+2  0 X+2  0  2  X  2  X  X  2  X  X  0  0  2  X  0 X+2  2 X+2  X  2  0  0  X  0 X+2  2 X+2  X  X  2  X  0  2  2  0  2  0  0  2  0  2 X+2  X  X X+2  0  2  X  X  0  0  2 X+2 X+2  0  0 X+2  2  X  X  2 X+2  2  0
 0  0  0  0  X  X  2 X+2  X X+2  2  2  X  2 X+2  X  X  2  2 X+2  0 X+2  0 X+2 X+2 X+2  0 X+2  0  X  0  2  0 X+2  X  0  2 X+2 X+2  0 X+2 X+2  0  2 X+2 X+2  0 X+2  0  2  0  2 X+2  2  X  X  2  X  0  2  X  0 X+2  0  X X+2  X  0 X+2  X  X  X  0 X+2  2  X  X  2 X+2 X+2  2 X+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+41x^76+62x^77+95x^78+134x^79+122x^80+168x^81+181x^82+190x^83+208x^84+178x^85+161x^86+122x^87+94x^88+72x^89+44x^90+46x^91+27x^92+22x^93+16x^94+16x^95+17x^96+8x^97+14x^98+4x^99+2x^101+2x^104+1x^138

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 0.694 seconds.