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.